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

{"title":"Duality theorems for curves over local fields","authors":"A. Krishna, Jitendra Rathore, Samiron Sadhukhan","doi":"10.1090/btran/187","DOIUrl":"https://doi.org/10.1090/btran/187","url":null,"abstract":"We prove duality theorems for the étale cohomology of split tori on smooth curves over a local field of positive characteristic. In particular, we show that the classical Brauer–Manin pairing between the Brauer and Picard groups of smooth projective curves over such a field extends to arbitrary smooth curves over the field. As another consequence, we obtain a description of the Brauer group of the function fields of curves over local fields in terms of the characters of the idele class groups.","PeriodicalId":377306,"journal":{"name":"Transactions of the American Mathematical Society, Series B","volume":"119 28","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141822267","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":"Density of continuous functions in Sobolev spaces with applications to capacity","authors":"S. Eriksson-Bique, Pietro Poggi-Corradini","doi":"10.1090/btran/188","DOIUrl":"https://doi.org/10.1090/btran/188","url":null,"abstract":"<p>We show that capacity can be computed with locally Lipschitz functions in locally complete and separable metric spaces. Further, we show that if <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis upper X comma d comma mu right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>X</mml:mi>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>d</mml:mi>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>μ</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">(X,d,mu )</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is a locally complete and separable metric measure space, then continuous functions are dense in the Newtonian space <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper N Superscript 1 comma p Baseline left-parenthesis upper X right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:msup>\u0000 <mml:mi>N</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>p</mml:mi>\u0000 </mml:mrow>\u0000 </mml:msup>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>X</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">N^{1,p}(X)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. Here the measure <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"mu\">\u0000 <mml:semantics>\u0000 <mml:mi>μ</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">mu</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is Borel and is finite and positive on all metric balls. In particular, we don’t assume properness of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\">\u0000 <mml:semantics>\u0000 <mml:mi>X</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">X</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>, doubling of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"mu\">\u0000 <mml:semantics>\u0000 <mml:mi>μ</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">mu</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> or any Poincaré inequalities. These resolve, partially or fully, questions posed by a number of authors, including J. Heinonen, A. Björn and J. Björn. In contrast to much of the past work, our results apply to <italic>locally complete</italic> spaces <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\">\u0000 <mml:semantics>\u0000 <mml:mi>X</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">X</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> an","PeriodicalId":377306,"journal":{"name":"Transactions of the American Mathematical Society, Series B","volume":"19 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141655136","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":"𝐶⁰-limits of Legendrian knots","authors":"Georgios Dimitroglou Rizell, Michael Sullivan","doi":"10.1090/btran/189","DOIUrl":"https://doi.org/10.1090/btran/189","url":null,"abstract":"Take a sequence of contactomorphisms of a contact three-manifold that \u0000\u0000 \u0000 \u0000 C\u0000 0\u0000 \u0000 C^0\u0000 \u0000\u0000-converges to a homeomorphism. If the images of a Legendrian knot limit to a smooth knot under this sequence, we show that it is contactomorphic to the original knot. We prove this by establishing that, on one hand, non–Legendrian knots admit a type of contact-squashing (similar to squeezing) onto transverse knots while, on the other hand, Legendrian knots do not admit such a squashing. The non-trivial input from contact topology that is needed is (a local version of) the Thurston–Bennequin inequality.","PeriodicalId":377306,"journal":{"name":"Transactions of the American Mathematical Society, Series B","volume":" 46","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140683900","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":"Multiple orthogonal polynomials, 𝑑-orthogonal polynomials, production matrices, and branched continued fractions","authors":"Alan Sokal","doi":"10.1090/btran/133","DOIUrl":"https://doi.org/10.1090/btran/133","url":null,"abstract":"I analyze an unexpected connection between multiple orthogonal polynomials, \u0000\u0000 \u0000 d\u0000 d\u0000 \u0000\u0000-orthogonal polynomials, production matrices and branched continued fractions. This work can be viewed as a partial extension of Viennot’s combinatorial theory of orthogonal polynomials to the case where the production matrix is lower-Hessenberg but is not necessarily tridiagonal.","PeriodicalId":377306,"journal":{"name":"Transactions of the American Mathematical Society, Series B","volume":"31 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140713373","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":"Closed 𝑘-Schur Katalan functions as 𝐾-homology Schubert representatives of the affine Grassmannian","authors":"Takeshi Ikeda, Shinsuke Iwao, Satoshi Naito","doi":"10.1090/btran/184","DOIUrl":"https://doi.org/10.1090/btran/184","url":null,"abstract":"Recently, Blasiak–Morse–Seelinger introduced symmetric func- tions called Katalan functions, and proved that the \u0000\u0000 \u0000 K\u0000 K\u0000 \u0000\u0000-theoretic \u0000\u0000 \u0000 k\u0000 k\u0000 \u0000\u0000-Schur functions due to Lam–Schilling–Shimozono form a subfamily of the Katalan functions. They conjectured that another subfamily of Katalan functions called closed \u0000\u0000 \u0000 k\u0000 k\u0000 \u0000\u0000-Schur Katalan functions is identified with the Schubert structure sheaves in the \u0000\u0000 \u0000 K\u0000 K\u0000 \u0000\u0000-homology of the affine Grassmannian. Our main result is a proof of this conjecture.\u0000\u0000We also study a \u0000\u0000 \u0000 K\u0000 K\u0000 \u0000\u0000-theoretic Peterson isomorphism that Ikeda, Iwao, and Maeno constructed, in a nongeometric manner, based on the unipotent solution of the relativistic Toda lattice of Ruijsenaars. We prove that the map sends a Schubert class of the quantum \u0000\u0000 \u0000 K\u0000 K\u0000 \u0000\u0000-theory ring of the flag variety to a closed \u0000\u0000 \u0000 K\u0000 K\u0000 \u0000\u0000-\u0000\u0000 \u0000 k\u0000 k\u0000 \u0000\u0000-Schur Katalan function up to an explicit factor related to a translation element with respect to an antidominant coroot. In fact, we prove this map coincides with a map whose existence was conjectured by Lam, Li, Mihalcea, Shimozono, and proved by Kato, and more recently by Chow and Leung.","PeriodicalId":377306,"journal":{"name":"Transactions of the American Mathematical Society, Series B","volume":"133 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140251399","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":"Property G and the 4-genus","authors":"Yi Ni","doi":"10.1090/btran/153","DOIUrl":"https://doi.org/10.1090/btran/153","url":null,"abstract":"<p>We say a null-homologous knot <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> in a <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"3\">\u0000 <mml:semantics>\u0000 <mml:mn>3</mml:mn>\u0000 <mml:annotation encoding=\"application/x-tex\">3</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-manifold <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper Y\">\u0000 <mml:semantics>\u0000 <mml:mi>Y</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">Y</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> has Property G, if the Thurston norm and fiberedness of the complement 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> is preserved under the zero surgery on <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>. In this paper, we will show that, if the smooth <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"4\">\u0000 <mml:semantics>\u0000 <mml:mn>4</mml:mn>\u0000 <mml:annotation encoding=\"application/x-tex\">4</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-genus of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper K times StartSet 0 EndSet\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>K</mml:mi>\u0000 <mml:mo>×<!-- × --></mml:mo>\u0000 <mml:mo fence=\"false\" stretchy=\"false\">{</mml:mo>\u0000 <mml:mn>0</mml:mn>\u0000 <mml:mo fence=\"false\" stretchy=\"false\">}</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">Ktimes {0}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> (in a certain homology class) in <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis upper Y times left-bracket 0 comma 1 right-bracket right-parenthesis number-sign upper N ModifyingAbove double-struck upper C upper P squared With bar\">\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:mo stretchy=\"false\">[</mml:mo>\u0000 <mml:mn>0</mml:mn>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mo stretchy=\"false\">]</mml:mo>\u0000 ","PeriodicalId":377306,"journal":{"name":"Transactions of the American Mathematical Society, Series B","volume":"48 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139533209","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 of line bundles on the incidence correspondence","authors":"Z. Gao, Claudiu Raicu","doi":"10.1090/btran/173","DOIUrl":"https://doi.org/10.1090/btran/173","url":null,"abstract":"<p>For a finite dimensional vector space <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper V\">\u0000 <mml:semantics>\u0000 <mml:mi>V</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">V</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> of dimension <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>, we consider the incidence correspondence (or partial flag variety) <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X subset-of double-struck upper P upper V times double-struck upper P upper V Superscript logical-or\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>X</mml:mi>\u0000 <mml:mo>⊂<!-- ⊂ --></mml:mo>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">P</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mi>V</mml:mi>\u0000 <mml:mo>×<!-- × --></mml:mo>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">P</mml:mi>\u0000 </mml:mrow>\u0000 <mml:msup>\u0000 <mml:mi>V</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo>∨<!-- ∨ --></mml:mo>\u0000 </mml:mrow>\u0000 </mml:msup>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">Xsubset mathbb {P}V times mathbb {P}V^{vee }</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>, parametrizing pairs consisting of a point and a hyperplane containing it. We completely characterize the vanishing and non-vanishing behavior of the cohomology groups of line bundles on <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\">\u0000 <mml:semantics>\u0000 <mml:mi>X</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">X</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> in characteristic <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p greater-than 0\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>p</mml:mi>\u0000 <mml:mo>></mml:mo>\u0000 <mml:mn>0</mml:mn>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">p>0</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. If <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"n equals 3\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:mo>=</mml:mo>\u0000 <mml:mn>3</mml:mn>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">n=3</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> then <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\">\u0000 <mml:semantics>\u0000 <mml:mi>X</mml:m","PeriodicalId":377306,"journal":{"name":"Transactions of the American Mathematical Society, Series B","volume":"21 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139382985","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":"𝐿₁-distortion of Wasserstein metrics: A tale of two dimensions","authors":"F. Baudier, C. Gartland, T. Schlumprecht","doi":"10.1090/btran/143","DOIUrl":"https://doi.org/10.1090/btran/143","url":null,"abstract":"<p>By discretizing an argument of Kislyakov, Naor and Schechtman proved that the 1-Wasserstein metric over the planar grid <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-brace 0 comma 1 comma ellipsis comma n right-brace squared\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mo fence=\"false\" stretchy=\"false\">{</mml:mo>\u0000 <mml:mn>0</mml:mn>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mo>…<!-- … --></mml:mo>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:msup>\u0000 <mml:mo fence=\"false\" stretchy=\"false\">}</mml:mo>\u0000 <mml:mn>2</mml:mn>\u0000 </mml:msup>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">{0,1,dots , n}^2</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> has <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L 1\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mi>L</mml:mi>\u0000 <mml:mn>1</mml:mn>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">L_1</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-distortion bounded below by a constant multiple of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"StartRoot log n EndRoot\">\u0000 <mml:semantics>\u0000 <mml:msqrt>\u0000 <mml:mi>log</mml:mi>\u0000 <mml:mo>⁡<!-- ⁡ --></mml:mo>\u0000 <mml:mi>n</mml:mi>\u0000 </mml:msqrt>\u0000 <mml:annotation encoding=\"application/x-tex\">sqrt {log n}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. We provide a new “dimensionality” interpretation of Kislyakov’s argument, showing that if <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-brace upper G Subscript n Baseline right-brace Subscript n equals 1 Superscript normal infinity\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mo fence=\"false\" stretchy=\"false\">{</mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:mi>n</mml:mi>\u0000 </mml:msub>\u0000 <mml:msubsup>\u0000 <mml:mo fence=\"false\" stretchy=\"false\">}</mml:mo>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi>n</mml:mi>\u0000 <mml:mo>=</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 </mml:mrow>\u0000 <mml:mi mathvariant=\"normal\">∞<!-- ∞ --></mml:mi>\u0000 </mml:msubsup>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">{G_n}_{n=1}^infty</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is a sequence of graphs whose isoperimetric dimension and Lipschitz-spectral dimension equal a common number <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"delta element-of left-bracket 2 comma normal infinity right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>δ<!-- δ --></mml:mi>\u0000 <mml:mo>∈<!-- ∈ --></mml:mo>\u0000 <mml:mo stretchy=\"fals","PeriodicalId":377306,"journal":{"name":"Transactions of the American Mathematical Society, Series B","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122085201","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":"Lattice theory of torsion classes: Beyond 𝜏-tilting theory","authors":"Laurent Demonet, O. Iyama, Nathan Reading, I. Reiten, Hugh Thomas","doi":"10.1090/btran/100","DOIUrl":"https://doi.org/10.1090/btran/100","url":null,"abstract":"<p>The aim of this paper is to establish a lattice theoretical framework to study the partially ordered set <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"sans-serif t sans-serif o sans-serif r sans-serif s upper A\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"sans-serif\">t</mml:mi>\u0000 <mml:mi mathvariant=\"sans-serif\">o</mml:mi>\u0000 <mml:mi mathvariant=\"sans-serif\">r</mml:mi>\u0000 <mml:mi mathvariant=\"sans-serif\">s</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mi>A</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">mathsf {tors} A</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> of torsion classes over a finite-dimensional algebra <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper A\">\u0000 <mml:semantics>\u0000 <mml:mi>A</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">A</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. We show that <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"sans-serif t sans-serif o sans-serif r sans-serif s upper A\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"sans-serif\">t</mml:mi>\u0000 <mml:mi mathvariant=\"sans-serif\">o</mml:mi>\u0000 <mml:mi mathvariant=\"sans-serif\">r</mml:mi>\u0000 <mml:mi mathvariant=\"sans-serif\">s</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mi>A</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">mathsf {tors} A</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is a complete lattice which enjoys very strong properties, as <italic>bialgebraicity</italic> and <italic>complete semidistributivity</italic>. Thus its Hasse quiver carries the important part of its structure, and we introduce the brick labelling of its Hasse quiver and use it to study lattice congruences of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"sans-serif t sans-serif o sans-serif r sans-serif s upper A\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"sans-serif\">t</mml:mi>\u0000 <mml:mi mathvariant=\"sans-serif\">o</mml:mi>\u0000 <mml:mi mathvariant=\"sans-serif\">r</mml:mi>\u0000 <mml:mi mathvariant=\"sans-serif\">s</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mi>A</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">mathsf {tors} A</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. In particular, we give a representation-theoretical interpretation of the so-called <italic>forcing order</italic>, and we prove that <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"sans-serif t sans-serif o sans-serif r sans-serif s upper A","PeriodicalId":377306,"journal":{"name":"Transactions of the American Mathematical Society, Series B","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126322906","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":"The fundamental solution to Box_{𝑏} on quadric manifolds with nonzero eigenvalues","authors":"A. Boggess, A. Raich","doi":"10.1090/btran/121","DOIUrl":"https://doi.org/10.1090/btran/121","url":null,"abstract":"This paper is part of a continuing examination into the geometric and analytic properties of the Kohn Laplacian and its inverse on general quadric submanifolds of \u0000\u0000 \u0000 \u0000 \u0000 \u0000 C\u0000 \u0000 n\u0000 \u0000 ×\u0000 \u0000 \u0000 C\u0000 \u0000 m\u0000 \u0000 \u0000 mathbb {C}^ntimes mathbb {C}^m\u0000 \u0000\u0000. The goal of this article is explore the complex Green operator in the case that the eigenvalues of the directional Levi forms are nonvanishing. We (1) investigate the geometric conditions on \u0000\u0000 \u0000 M\u0000 M\u0000 \u0000\u0000 which the eigenvalue condition forces, (2) establish optimal pointwise upper bounds on complex Green operator and its derivatives, (3) explore the \u0000\u0000 \u0000 \u0000 L\u0000 p\u0000 \u0000 L^p\u0000 \u0000\u0000 and \u0000\u0000 \u0000 \u0000 L\u0000 p\u0000 \u0000 L^p\u0000 \u0000\u0000-Sobolev mapping properties of the associated kernels, and (4) provide examples.","PeriodicalId":377306,"journal":{"name":"Transactions of the American Mathematical Society, Series B","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131185924","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}