Transactions of the American Mathematical Society, Series B最新文献

{"title":"Rational curves on del Pezzo surfaces in positive characteristic","authors":"Roya Beheshti, Brian Lehmann, Eric Riedl, Sho Tanimoto","doi":"10.1090/btran/138","DOIUrl":"https://doi.org/10.1090/btran/138","url":null,"abstract":"<p>We study the space of rational curves on del Pezzo surfaces in positive characteristic. For most primes <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p\">\u0000 <mml:semantics>\u0000 <mml:mi>p</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">p</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> we prove the irreducibility of the moduli space of rational curves of a given nef class, extending results of Testa in characteristic <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"0\">\u0000 <mml:semantics>\u0000 <mml:mn>0</mml:mn>\u0000 <mml:annotation encoding=\"application/x-tex\">0</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. We also investigate the principles of Geometric Manin’s Conjecture for weak del Pezzo surfaces. In the course of this investigation, we give examples of weak del Pezzo surfaces defined over <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper F 2 left-parenthesis t right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:msub>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">F</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mn>2</mml:mn>\u0000 </mml:msub>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>t</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">mathbb F_2(t)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> or <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper F 3 left-parenthesis t right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:msub>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">F</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mn>3</mml:mn>\u0000 </mml:mrow>\u0000 </mml:msub>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>t</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">mathbb {F}_{3}(t)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> such that the exceptional sets in Manin’s Conjecture are Zariski dense.</p>","PeriodicalId":377306,"journal":{"name":"Transactions of the American Mathematical Society, Series B","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131259596","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Varieties of general type with doubly exponential asymptotics","authors":"L. Esser, B. Totaro, Chengxi Wang","doi":"10.1090/btran/125","DOIUrl":"https://doi.org/10.1090/btran/125","url":null,"abstract":"We construct smooth projective varieties of general type with the smallest known volume and others with the most known vanishing plurigenera in high dimensions. The optimal volume bound is expected to decay doubly exponentially with dimension, and our examples achieve this decay rate. We also consider the analogous questions for other types of varieties. For example, in every dimension we conjecture the terminal Fano variety of minimal volume, and the canonical Calabi-Yau variety of minimal volume. In each case, our examples exhibit doubly exponential behavior.","PeriodicalId":377306,"journal":{"name":"Transactions of the American Mathematical Society, Series B","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133077070","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Ricci curvature integrals, local functionals, and the Ricci flow","authors":"Yuanqing Ma, Bing Wang","doi":"10.1090/btran/155","DOIUrl":"https://doi.org/10.1090/btran/155","url":null,"abstract":"<p>Consider a Riemannian manifold <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis upper M Superscript m Baseline comma g right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mo stretchy=\"false\">(</mml:mo> <mml:msup> <mml:mi>M</mml:mi> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi>m</mml:mi> </mml:mrow> </mml:msup> <mml:mo>,</mml:mo> <mml:mi>g</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">(M^{m}, g)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> whose volume is the same as the standard sphere <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis upper S Superscript m Baseline comma g Subscript r o u n d Baseline right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mo stretchy=\"false\">(</mml:mo> <mml:msup> <mml:mi>S</mml:mi> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi>m</mml:mi> </mml:mrow> </mml:msup> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>g</mml:mi> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi>r</mml:mi> <mml:mi>o</mml:mi> <mml:mi>u</mml:mi> <mml:mi>n</mml:mi> <mml:mi>d</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">(S^{m}, g_{round})</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. If <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p greater-than StartFraction m Over 2 EndFraction\"> <mml:semantics> <mml:mrow> <mml:mi>p</mml:mi> <mml:mspace width=\"negativethinmathspace\" /> <mml:mo>></mml:mo> <mml:mspace width=\"negativethinmathspace\" /> <mml:mfrac> <mml:mi>m</mml:mi> <mml:mn>2</mml:mn> </mml:mfrac> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">p!>!frac {m}{2}</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=\"integral Underscript upper M Endscripts left-brace upper R c minus left-parenthesis m minus 1 right-parenthesis g right-brace Subscript minus Superscript p Baseline d v\"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mo>∫<!-- ∫ --></mml:mo> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi>M</mml:mi> </mml:mrow> </mml:msub> <mml:mspace width=\"negativethinmathspace\" /> <mml:msubsup> <mml:mrow> <mml:mo>{</mml:mo> <mml:mi>R</mml:mi> <mml:mi>c</mml:mi> <mm","PeriodicalId":377306,"journal":{"name":"Transactions of the American Mathematical Society, Series B","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129496820","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On Floer minimal knots in sutured manifolds","authors":"Zhenkun Li, Yi Xie, Boyu Zhang","doi":"10.1090/btran/105","DOIUrl":"https://doi.org/10.1090/btran/105","url":null,"abstract":"<p>Suppose <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis upper M comma gamma right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>M</mml:mi>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>γ<!-- γ --></mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">(M, gamma )</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is a balanced sutured manifold and <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper K\">\u0000 <mml:semantics>\u0000 <mml:mi>K</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">K</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is a rationally null-homologous knot in <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper M\">\u0000 <mml:semantics>\u0000 <mml:mi>M</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">M</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. It is known that the rank of the sutured Floer homology of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper M minus upper N left-parenthesis upper K right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>M</mml:mi>\u0000 <mml:mi class=\"MJX-variant\" mathvariant=\"normal\">∖<!-- ∖ --></mml:mi>\u0000 <mml:mi>N</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>K</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">Mbackslash N(K)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is at least twice the rank of the sutured Floer homology of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper M\">\u0000 <mml:semantics>\u0000 <mml:mi>M</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">M</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. This paper studies the properties of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper K\">\u0000 <mml:semantics>\u0000 <mml:mi>K</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">K</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> when the equality is achieved for instanton homology. As an application, we show that if <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L subset-of upper S cubed\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>L</mml:mi>\u0000 <mml:mo>⊂<!-- ⊂ --></mml:mo>\u0000 <mml:msup>\u0000 <mml:mi>S</mml:mi>\u0000 <mml:mn>3</mml:mn>\u0000 </mml:msup>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">Lsubset S^3</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000","PeriodicalId":377306,"journal":{"name":"Transactions of the American Mathematical Society, Series B","volume":"79 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126337158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Volume bound for the canonical lift complement of a random geodesic","authors":"Tommaso Cremaschi, Yannick Krifka, D'idac Mart'inez-Granado, Franco Vargas Pallete","doi":"10.1090/btran/152","DOIUrl":"https://doi.org/10.1090/btran/152","url":null,"abstract":"Given a filling primitive geodesic curve in a closed hyperbolic surface one obtains a hyperbolic three-manifold as the complement of the curve's canonical lift to the projective tangent bundle. In this paper we give the first known lower bound for the volume of these manifolds in terms of the length of generic curves. We show that estimating the volume from below can be reduced to a counting problem in the unit tangent bundle and solve it by applying an exponential multiple mixing result for the geodesic flow.","PeriodicalId":377306,"journal":{"name":"Transactions of the American Mathematical Society, Series B","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127541427","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Equi-Lipschitz minimizing trajectories for non coercive, discontinuous, non convex Bolza controlled-linear optimal control problems","authors":"C. Mariconda","doi":"10.1090/btran/80","DOIUrl":"https://doi.org/10.1090/btran/80","url":null,"abstract":"<p>This article deals with the Lipschitz regularity of the “approximate” minimizers for the Bolza type control functional of the form <disp-formula content-type=\"math/mathml\">\u0000[\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper J Subscript t Baseline left-parenthesis y comma u right-parenthesis colon-equal integral Subscript t Superscript upper T Baseline normal upper Lamda left-parenthesis s comma y left-parenthesis s right-parenthesis comma u left-parenthesis s right-parenthesis right-parenthesis d s plus g left-parenthesis y left-parenthesis upper T right-parenthesis right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:msub>\u0000 <mml:mi>J</mml:mi>\u0000 <mml:mi>t</mml:mi>\u0000 </mml:msub>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>y</mml:mi>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>u</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mo>≔</mml:mo>\u0000 <mml:msubsup>\u0000 <mml:mo>∫<!-- ∫ --></mml:mo>\u0000 <mml:mi>t</mml:mi>\u0000 <mml:mi>T</mml:mi>\u0000 </mml:msubsup>\u0000 <mml:mi mathvariant=\"normal\">Λ<!-- Λ --></mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>s</mml:mi>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>y</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>s</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>u</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>s</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mspace width=\"thinmathspace\" />\u0000 <mml:mi>d</mml:mi>\u0000 <mml:mi>s</mml:mi>\u0000 <mml:mo>+</mml:mo>\u0000 <mml:mi>g</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>y</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>T</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">J_t(y,u)≔int _t^TLambda (s,y(s), u(s)),ds+g(y(T))</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000]\u0000</disp-formula> among the pairs <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis y comma u right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>y</mml:mi>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>u</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">(y,u)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> satisfying a prescribed initial condition <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"y left-parenthesis t right-parenthesis equals x\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>y</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>t</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mo>=</mml:mo>\u0000 <mml:mi>x</mml:m","PeriodicalId":377306,"journal":{"name":"Transactions of the American Mathematical Society, Series B","volume":"139 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123251146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Critical point counts in knot cobordisms: abelian and metacyclic invariants","authors":"C. Livingston","doi":"10.1090/btran/139","DOIUrl":"https://doi.org/10.1090/btran/139","url":null,"abstract":"<p>For a pair of knots <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper K 1\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mi>K</mml:mi>\u0000 <mml:mn>1</mml:mn>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">K_1</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> and <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper K 0\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mi>K</mml:mi>\u0000 <mml:mn>0</mml:mn>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">K_0</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>, we consider the set of four-tuples of integers <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis g comma c 0 comma c 1 comma c 2 right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>g</mml:mi>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>c</mml:mi>\u0000 <mml:mn>0</mml:mn>\u0000 </mml:msub>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>c</mml:mi>\u0000 <mml:mn>1</mml:mn>\u0000 </mml:msub>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>c</mml:mi>\u0000 <mml:mn>2</mml:mn>\u0000 </mml:msub>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">(g, c_0,c_1, c_2)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> for which there is a cobordism from <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper K 1\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mi>K</mml:mi>\u0000 <mml:mn>1</mml:mn>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">K_1</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> to <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper K 0\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mi>K</mml:mi>\u0000 <mml:mn>0</mml:mn>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">K_0</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> of genus <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"g\">\u0000 <mml:semantics>\u0000 <mml:mi>g</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">g</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> having <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"c Subscript i\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mi>c</mml:mi>\u0000 <mml:mi>i</mml:mi>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">c_i</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> critical points of each index <inline-formula content-type=\"math/mathml\">\u0000<mml:mat","PeriodicalId":377306,"journal":{"name":"Transactions of the American Mathematical Society, Series B","volume":"37 36","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114047058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Cohomology ring of tree braid groups and exterior face rings","authors":"Jes'us Gonz'alez, Teresa I. Hoekstra-Mendoza","doi":"10.1090/btran/131","DOIUrl":"https://doi.org/10.1090/btran/131","url":null,"abstract":"<p>For a tree <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper T\">\u0000 <mml:semantics>\u0000 <mml:mi>T</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">T</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> and a positive integer <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"n\">\u0000 <mml:semantics>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">n</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>, let <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper B Subscript n Baseline upper T\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:msub>\u0000 <mml:mi>B</mml:mi>\u0000 <mml:mi>n</mml:mi>\u0000 </mml:msub>\u0000 <mml:mi>T</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">B_nT</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> denote the <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"n\">\u0000 <mml:semantics>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">n</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-strand braid group on <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper T\">\u0000 <mml:semantics>\u0000 <mml:mi>T</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">T</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. We use discrete Morse theory techniques to show that the cohomology ring <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper H Superscript asterisk Baseline left-parenthesis upper B Subscript n Baseline upper T right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:msup>\u0000 <mml:mi>H</mml:mi>\u0000 <mml:mo>∗<!-- ∗ --></mml:mo>\u0000 </mml:msup>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>B</mml:mi>\u0000 <mml:mi>n</mml:mi>\u0000 </mml:msub>\u0000 <mml:mi>T</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">H^*(B_nT)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is encoded by an explicit abstract simplicial complex <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper K Subscript n Baseline upper T\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:msub>\u0000 <mml:mi>K</mml:mi>\u0000 <mml:mi>n</mml:mi>\u0000 </mml:msub>\u0000 <mml:mi>T</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">K_nT</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> that measures <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"n\">\u0000 <mml:seman","PeriodicalId":377306,"journal":{"name":"Transactions of the American Mathematical Society, Series B","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123008913","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Shift modules, strongly stable ideals, and their dualities","authors":"Gunnar Fløystad","doi":"10.1090/btran/137","DOIUrl":"https://doi.org/10.1090/btran/137","url":null,"abstract":"We enrich the setting of strongly stable ideals (SSI): We introduce shift modules, a module category encompassing SSIs. The recently introduced duality on SSIs is given an effective conceptual and computational setting. We study SSIs in infinite dimensional polynomial rings, where the duality is most natural. Finally a new type of resolution for SSIs is introduced. This is the projective resolution in the category of shift modules.","PeriodicalId":377306,"journal":{"name":"Transactions of the American Mathematical Society, Series B","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115016246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Characterizations of monadic NIP","authors":"S. Braunfeld, M. Laskowski","doi":"10.1090/btran/94","DOIUrl":"https://doi.org/10.1090/btran/94","url":null,"abstract":"We give several characterizations of when a complete first-order theory \u0000\u0000 \u0000 T\u0000 T\u0000 \u0000\u0000 is monadically NIP, i.e. when expansions of \u0000\u0000 \u0000 T\u0000 T\u0000 \u0000\u0000 by arbitrary unary predicates do not have the independence property. The central characterization is a condition on finite satisfiability of types. Other characterizations include decompositions of models, the behavior of indiscernibles, and a forbidden configuration. As an application, we prove non-structure results for hereditary classes of finite substructures of non-monadically NIP models that eliminate quantifiers.","PeriodicalId":377306,"journal":{"name":"Transactions of the American Mathematical Society, Series B","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125554880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}