Transactions of the American Mathematical Society最新文献

{"title":"The ratios conjecture for real Dirichlet characters and multiple Dirichlet series","authors":"Martin Čech","doi":"10.1090/tran/9113","DOIUrl":"https://doi.org/10.1090/tran/9113","url":null,"abstract":"<p>Conrey, Farmer and Zirnbauer introduced a recipe to find asymptotic formulas for the sum of ratios of products of shifted L-functions. These ratios conjectures are very powerful and can be used to determine many statistics of L-functions, including moments or statistics about the distribution of zeros.</p> <p>We consider the family of real Dirichlet characters, and use multiple Dirichlet series to prove the ratios conjectures with one shift in the numerator and denominator in some range of the shifts. This range can be improved by extending the family to include non-primitive characters. All of the results are conditional under the Generalized Riemann hypothesis.</p> <p>This extended range is good enough to enable us to compute an asymptotic formula for the sum of shifted logarithmic derivatives near the critical line. As an application, we compute the one-level density for test functions whose Fourier transform is supported in <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis negative 2 comma 2 right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mo>(</mml:mo> <mml:mo>−<!-- − --></mml:mo> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">left (-2,2right )</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, including lower-order terms.</p>","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140934796","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"BPS invariants of symplectic log Calabi-Yau fourfolds","authors":"Mohammad Farajzadeh-Tehrani","doi":"10.1090/tran/9114","DOIUrl":"https://doi.org/10.1090/tran/9114","url":null,"abstract":"<p>Using the Fredholm setup of Farajzadeh-Tehrani [Peking Math. J. (2023), https://doi.org/10.1007/s42543-023-00069-1], we study genus zero (and higher) relative Gromov-Witten invariants with maximum tangency of symplectic log Calabi-Yau fourfolds. In particular, we give a short proof of Gross [Duke Math. J. 153 (2010), pp. 297–362, Cnj. 6.2] that expresses these invariants in terms of certain integral invariants by considering generic almost complex structures to obtain a geometric count. We also revisit the localization calculation of the multiple-cover contributions in Gross [Prp. 6.1] and recalculate a few terms differently to provide more details and illustrate the computation of deformation/obstruction spaces for maps that have components in a destabilizing (or rubber) component of the target. Finally, we study a higher genus version of these invariants and explain a decomposition of genus one invariants into different contributions.</p>","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140934798","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the constant of Lipschitz approximability","authors":"Rubén Medina","doi":"10.1090/tran/9110","DOIUrl":"https://doi.org/10.1090/tran/9110","url":null,"abstract":"<p>In this note we find <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"lamda greater-than 1\"> <mml:semantics> <mml:mrow> <mml:mi>λ<!-- λ --></mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">lambda &gt;1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and give an explicit construction of a separable Banach space <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=\"application/x-tex\">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> such that there is no <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"lamda\"> <mml:semantics> <mml:mi>λ<!-- λ --></mml:mi> <mml:annotation encoding=\"application/x-tex\">lambda</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-Lipschitz retraction from <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=\"application/x-tex\">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> onto any compact convex subset of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=\"application/x-tex\">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> whose closed linear span is <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=\"application/x-tex\">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. This is closely related to a well-known open problem raised by Godefroy and Ozawa in 2014 and represents the first known example of a Banach space with such a property.</p>","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140934867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Higher rank (𝑞,𝑡)-Catalan polynomials, affine Springer fibers, and a finite rational shuffle theorem","authors":"Nicolle González, José Simental, Monica Vazirani","doi":"10.1090/tran/9115","DOIUrl":"https://doi.org/10.1090/tran/9115","url":null,"abstract":"<p>We introduce the higher rank <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis q comma t right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>q</mml:mi> <mml:mo>,</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">(q,t)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-Catalan polynomials and prove they equal truncations of the Hikita polynomial to a finite number of variables. Using affine compositions and a certain standardization map, we define a <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"monospace d monospace i monospace n monospace v\"> <mml:semantics> <mml:mrow> <mml:mi mathvariant=\"monospace\">d</mml:mi> <mml:mi mathvariant=\"monospace\">i</mml:mi> <mml:mi mathvariant=\"monospace\">n</mml:mi> <mml:mi mathvariant=\"monospace\">v</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">mathtt {dinv}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> statistic on rank <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"r\"> <mml:semantics> <mml:mi>r</mml:mi> <mml:annotation encoding=\"application/x-tex\">r</mml:annotation> </mml:semantics> </mml:math> </inline-formula> semistandard <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis m comma n right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>m</mml:mi> <mml:mo>,</mml:mo> <mml:mi>n</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">(m,n)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-parking functions and prove <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"monospace c monospace o monospace d monospace i monospace n monospace v\"> <mml:semantics> <mml:mrow> <mml:mi mathvariant=\"monospace\">c</mml:mi> <mml:mi mathvariant=\"monospace\">o</mml:mi> <mml:mi mathvariant=\"monospace\">d</mml:mi> <mml:mi mathvariant=\"monospace\">i</mml:mi> <mml:mi mathvariant=\"monospace\">n</mml:mi> <mml:mi mathvariant=\"monospace\">v</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">mathtt {codinv}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> counts the dimension of an affine space in an affine paving of a parabolic affine Springer fiber. Combining these results, we give a finite analogue of the Rational Shuffle Theorem in the context of double affine Hecke algebras. Lastly, we also give a Bizley-type formula for the higher rank Catalan numbers in the non-coprime case.</p>","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141060602","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Weierstrass bridges","authors":"Alexander Schied, Zhenyuan Zhang","doi":"10.1090/tran/9116","DOIUrl":"https://doi.org/10.1090/tran/9116","url":null,"abstract":"<p>We introduce a new class of stochastic processes called fractional Wiener–Weierstraß bridges. They arise by applying the convolution from the construction of the classical, fractal Weierstraß functions to an underlying fractional Brownian bridge. By analyzing the <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p\"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding=\"application/x-tex\">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-th variation of the fractional Wiener–Weierstraß bridge along the sequence of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"b\"> <mml:semantics> <mml:mi>b</mml:mi> <mml:annotation encoding=\"application/x-tex\">b</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-adic partitions, we identify two regimes in which the processes exhibit distinct sample path properties. We also analyze the critical case between those two regimes for Wiener–Weierstraß bridges that are based on a standard Brownian bridge. We furthermore prove that fractional Wiener–Weierstraß bridges are never semimartingales, and we show that their covariance functions are typically fractal functions. Some of our results are extended to Weierstraß bridges based on bridges derived from a general continuous Gaussian martingale.</p>","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140935215","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the rôle of singular functions in extending the probabilistic symbol to its most general class","authors":"Sebastian Rickelhoff, Alexander Schnurr","doi":"10.1090/tran/9064","DOIUrl":"https://doi.org/10.1090/tran/9064","url":null,"abstract":"The probabilistic symbol is the right-hand side derivative of the characteristic functions corresponding to the one-dimensional marginals of a stochastic process. This object, as long as the derivative exists, provides crucial information concerning the stochastic process. For a Lévy process, one obtains the characteristic exponent while the symbol of a (rich) Feller process coincides with the classical symbol which is well known from the theory of pseudodifferential operators. Leaving these classes behind, the most general class of processes for which the symbol still exists are Lévy-type processes. It has been an open question, whether further generalizations are possible within the framework of Markov processes. We answer this question in the present article: within the class of Hunt semimartingales, Lévy-type processes are exactly those for which the probabilistic symbol exists. Leaving Hunt behind, one can construct processes admitting a symbol. However, we show, that the applicability of the symbol might be lost for these processes. Surprisingly, in our proofs the upper and lower Dini derivatives corresponding to certain singular functions play an important rôle.","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135191250","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A solution operator for the overline{∂} equation in Sobolev spaces of negative index","authors":"Ziming Shi, Liding Yao","doi":"10.1090/tran/9066","DOIUrl":"https://doi.org/10.1090/tran/9066","url":null,"abstract":"Let <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Omega\"> <mml:semantics> <mml:mi mathvariant=\"normal\">Ω<!-- Ω --></mml:mi> <mml:annotation encoding=\"application/x-tex\">Omega</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a strictly pseudoconvex domain in <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper C Superscript n\"> <mml:semantics> <mml:msup> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi mathvariant=\"double-struck\">C</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> <mml:annotation encoding=\"application/x-tex\">mathbb {C}^n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper C Superscript k plus 2\"> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi>k</mml:mi> <mml:mo>+</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:annotation encoding=\"application/x-tex\">C^{k+2}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> boundary, <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"k greater-than-or-equal-to 1\"> <mml:semantics> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>≥<!-- ≥ --></mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">k geq 1</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We construct a <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"ModifyingAbove partial-differential With bar\"> <mml:semantics> <mml:mover> <mml:mi mathvariant=\"normal\">∂<!-- ∂ --></mml:mi> <mml:mo accent=\"false\">¯<!-- ¯ --></mml:mo> </mml:mover> <mml:annotation encoding=\"application/x-tex\">overline partial</mml:annotation> </mml:semantics> </mml:math> </inline-formula> solution operator (depending on <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"k\"> <mml:semantics> <mml:mi>k</mml:mi> <mml:annotation encoding=\"application/x-tex\">k</mml:annotation> </mml:semantics> </mml:math> </inline-formula>) that gains <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"one half\"> <mml:semantics> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> <mml:annotation encoding=\"application/x-tex\">frac 12</mml:annotation> </mml:semantics> </mml:math> </inline-formula> derivative in the Sobolev space <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper H Superscript s comma p Baseline left-parenthesis normal upper Omega right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>H</mml:mi> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi>s</mml:mi> <mml:mo>,</mml:mo> <mml","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135191249","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Moduli spaces of Lie algebras and foliations","authors":"Sebastián Velazquez","doi":"10.1090/tran/9072","DOIUrl":"https://doi.org/10.1090/tran/9072","url":null,"abstract":"Let <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=\"application/x-tex\">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a smooth projective variety over the complex numbers and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper S left-parenthesis d right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>S</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>d</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">S(d)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> the scheme parametrizing <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"d\"> <mml:semantics> <mml:mi>d</mml:mi> <mml:annotation encoding=\"application/x-tex\">d</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-dimensional Lie subalgebras of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper H Superscript 0 Baseline left-parenthesis upper X comma script upper T upper X right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>H</mml:mi> <mml:mn>0</mml:mn> </mml:msup> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>,</mml:mo> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">T</mml:mi> </mml:mrow> <mml:mi>X</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">H^0(X,mathcal {T}X)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. This article is dedicated to the study of the geometry of the moduli space <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"Inv\"> <mml:semantics> <mml:mtext>Inv</mml:mtext> <mml:annotation encoding=\"application/x-tex\">text {Inv}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of involutive distributions on <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=\"application/x-tex\">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> around the points <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper F element-of Inv\"> <mml:semantics> <mml:mrow> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">F</mml:mi> </mml:mrow> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:mtext>Inv</mml:mtext> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">mathcal {F}in text {Inv}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> which are induced by Lie group actions. For every <inline-formula content-type=\"math/mathm","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135190995","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multisections of 4-manifolds","authors":"Gabriel Islambouli, Patrick Naylor","doi":"10.1090/tran/8996","DOIUrl":"https://doi.org/10.1090/tran/8996","url":null,"abstract":"We introduce multisections of smooth, closed 4-manifolds, which generalize trisections to decompositions with more than three pieces. This decomposition describes an arbitrary smooth, closed 4-manifold as a sequence of cut systems on a surface. We show how to carry out many smooth cut and paste operations in terms of these cut systems. In particular, we show how to implement a cork twist, whereby we show that an arbitrary exotic pair of smooth 4-manifolds admit 4-sections differing only by one cut system. By carrying out fiber sums and log transforms, we also show that the elliptic fibrations <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper E left-parenthesis n right-parenthesis Subscript p comma q\"> <mml:semantics> <mml:mrow> <mml:mi>E</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>n</mml:mi> <mml:msub> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi>p</mml:mi> <mml:mo>,</mml:mo> <mml:mi>q</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">E(n)_{p,q}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> all admit genus <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"3\"> <mml:semantics> <mml:mn>3</mml:mn> <mml:annotation encoding=\"application/x-tex\">3</mml:annotation> </mml:semantics> </mml:math> </inline-formula> multisections, and draw explicit diagrams for these manifolds.","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135191522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Products of normal subsets","authors":"Michael Larsen, Aner Shalev, Pham Tiep","doi":"10.1090/tran/8960","DOIUrl":"https://doi.org/10.1090/tran/8960","url":null,"abstract":"In this paper we consider which families of finite simple groups <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=\"application/x-tex\">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> have the property that for each <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"epsilon greater-than 0\"> <mml:semantics> <mml:mrow> <mml:mi>ϵ<!-- ϵ --></mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">epsilon &gt; 0</mml:annotation> </mml:semantics> </mml:math> </inline-formula> there exists <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper N greater-than 0\"> <mml:semantics> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">N &gt; 0</mml:annotation> </mml:semantics> </mml:math> </inline-formula> such that, if <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"StartAbsoluteValue upper G EndAbsoluteValue greater-than-or-equal-to upper N\"> <mml:semantics> <mml:mrow> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mo stretchy=\"false\">|</mml:mo> </mml:mrow> <mml:mi>G</mml:mi> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mo stretchy=\"false\">|</mml:mo> </mml:mrow> <mml:mo>≥<!-- ≥ --></mml:mo> <mml:mi>N</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">|G| ge N</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper S comma upper T\"> <mml:semantics> <mml:mrow> <mml:mi>S</mml:mi> <mml:mo>,</mml:mo> <mml:mi>T</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">S, T</mml:annotation> </mml:semantics> </mml:math> </inline-formula> are normal subsets of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=\"application/x-tex\">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with at least <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"epsilon StartAbsoluteValue upper G EndAbsoluteValue\"> <mml:semantics> <mml:mrow> <mml:mi>ϵ<!-- ϵ --></mml:mi> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mo stretchy=\"false\">|</mml:mo> </mml:mrow> <mml:mi>G</mml:mi> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mo stretchy=\"false\">|</mml:mo> </mml:mrow> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">epsilon |G|</mml:annotation> </mml:semantics> </mml:math> </inline-formula> elements each, then every non-trivial element of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://ww","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135340585","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}