Journal of the London Mathematical Society-Second Series最新文献

{"title":"On the diameter of semigroups of transformations and partitions","authors":"James East,&nbsp;Victoria Gould,&nbsp;Craig Miller,&nbsp;Thomas Quinn-Gregson,&nbsp;Nik Ruškuc","doi":"10.1112/jlms.12944","DOIUrl":"https://doi.org/10.1112/jlms.12944","url":null,"abstract":"<p>For a semigroup <span></span><math>\u0000 <semantics>\u0000 <mi>S</mi>\u0000 <annotation>$S$</annotation>\u0000 </semantics></math> whose universal right congruence is finitely generated (or, equivalently, a semigroup satisfying the homological finiteness property of being type right-<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>F</mi>\u0000 <msub>\u0000 <mi>P</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$FP_1$</annotation>\u0000 </semantics></math>), the right diameter of <span></span><math>\u0000 <semantics>\u0000 <mi>S</mi>\u0000 <annotation>$S$</annotation>\u0000 </semantics></math> is a parameter that expresses how ‘far apart’ elements of <span></span><math>\u0000 <semantics>\u0000 <mi>S</mi>\u0000 <annotation>$S$</annotation>\u0000 </semantics></math> can be from each other, in a certain sense. To be more precise, for each finite generating set <span></span><math>\u0000 <semantics>\u0000 <mi>U</mi>\u0000 <annotation>$U$</annotation>\u0000 </semantics></math> for the universal right congruence on <span></span><math>\u0000 <semantics>\u0000 <mi>S</mi>\u0000 <annotation>$S$</annotation>\u0000 </semantics></math>, we have a metric space <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>S</mi>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>d</mi>\u0000 <mi>U</mi>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(S,d_U)$</annotation>\u0000 </semantics></math> where <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>d</mi>\u0000 <mi>U</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>a</mi>\u0000 <mo>,</mo>\u0000 <mi>b</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$d_U(a,b)$</annotation>\u0000 </semantics></math> is the minimum length of derivations for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>a</mi>\u0000 <mo>,</mo>\u0000 <mi>b</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(a,b)$</annotation>\u0000 </semantics></math> as a consequence of pairs in <span></span><math>\u0000 <semantics>\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12944","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141326634","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Relatively Anosov representations via flows II: Examples","authors":"Feng Zhu,&nbsp;Andrew Zimmer","doi":"10.1112/jlms.12949","DOIUrl":"https://doi.org/10.1112/jlms.12949","url":null,"abstract":"<p>This is the second in a series of two papers that develops a theory of relatively Anosov representations using the original “contracting flow on a bundle” definition of Anosov representations introduced by Labourie and Guichard–Wienhard. In this paper, we focus on building families of examples.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12949","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141304233","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Topological recursion for Kadomtsev–Petviashvili tau functions of hypergeometric type","authors":"Boris Bychkov,&nbsp;Petr Dunin-Barkowski,&nbsp;Maxim Kazarian,&nbsp;Sergey Shadrin","doi":"10.1112/jlms.12946","DOIUrl":"https://doi.org/10.1112/jlms.12946","url":null,"abstract":"<p>We study the <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>-point differentials corresponding to Kadomtsev–Petviashvili (KP) tau functions of hypergeometric type (also known as Orlov–Scherbin partition functions), with an emphasis on their <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>ℏ</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$hbar ^2$</annotation>\u0000 </semantics></math>-deformations and expansions. Under the naturally required analytic assumptions, we prove certain higher loop equations that, in particular, contain the standard linear and quadratic loop equations, and thus imply the blobbed topological recursion. We also distinguish two large families of the Orlov–Scherbin partition functions that do satisfy the natural analytic assumptions, and for these families, we prove in addition the so-called projection property and thus the full statement of the Chekhov–Eynard–Orantin topological recursion. A particular feature of our argument is that it clarifies completely the role of <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>ℏ</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$hbar ^2$</annotation>\u0000 </semantics></math>-deformations of the Orlov–Scherbin parameters for the partition functions, whose necessity was known from a variety of earlier obtained results in this direction but never properly understood in the context of topological recursion. As special cases of the results of this paper, one recovers new and uniform proofs of the topological recursion to all previously studied cases of enumerative problems related to weighted double Hurwitz numbers. By virtue of topological recursion and the Grothendieck–Riemann–Roch formula, this, in turn, gives new and uniform proofs of almost all Ekedahl–Lando–Shapiro–Vainshtein (ELSV)-type formulas discussed in the literature.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12946","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141286821","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Characterizing slopes for \u0000 \u0000 \u0000 5\u0000 2\u0000 \u0000 $5_2$","authors":"John A. Baldwin,&nbsp;Steven Sivek","doi":"10.1112/jlms.12951","DOIUrl":"https://doi.org/10.1112/jlms.12951","url":null,"abstract":"<p>We prove that all rational slopes are characterizing for the knot <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mn>5</mn>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <annotation>$5_2$</annotation>\u0000 </semantics></math>, except possibly for positive integers. Along the way, we classify the Dehn surgeries on knots in <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mn>3</mn>\u0000 </msup>\u0000 <annotation>$S^3$</annotation>\u0000 </semantics></math> that produce the Brieskorn sphere <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Σ</mi>\u0000 <mo>(</mo>\u0000 <mn>2</mn>\u0000 <mo>,</mo>\u0000 <mn>3</mn>\u0000 <mo>,</mo>\u0000 <mn>11</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$Sigma (2,3,11)$</annotation>\u0000 </semantics></math>, and we study knots on which large integral surgeries are almost L-spaces.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141286788","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":"Uniform rational polytopes of foliated threefolds and the global ACC","authors":"Jihao Liu,&nbsp;Fanjun Meng,&nbsp;Lingyao Xie","doi":"10.1112/jlms.12950","DOIUrl":"https://doi.org/10.1112/jlms.12950","url":null,"abstract":"<p>In this paper, we show the existence of uniform rational lc polytopes for foliations with functional boundaries in dimension <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>⩽</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$leqslant 3$</annotation>\u0000 </semantics></math>. As an application, we prove the global ACC for foliated threefolds with arbitrary DCC coefficients. We also provide applications on the accumulation points of lc thresholds of foliations in dimension <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>⩽</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$leqslant 3$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141251293","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":"Local behavior of the mixed local and nonlocal problems with nonstandard growth","authors":"Mengyao Ding,&nbsp;Yuzhou Fang,&nbsp;Chao Zhang","doi":"10.1112/jlms.12947","DOIUrl":"https://doi.org/10.1112/jlms.12947","url":null,"abstract":"<p>We consider the mixed local and nonlocal functionals with nonstandard growth\u0000\u0000 </p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141251294","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":"Solutions with multiple interfaces to the generalized parabolic Cahn–Hilliard equation in one and three space dimensions","authors":"Chao Liu,&nbsp;Jun Yang","doi":"10.1112/jlms.12941","DOIUrl":"https://doi.org/10.1112/jlms.12941","url":null,"abstract":"<p>We consider the generalized parabolic Cahn–Hilliard equation\u0000\u0000 </p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141245662","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":"Morita equivalence classes of 2-blocks with abelian defect groups of rank 4","authors":"Charles W. Eaton,&nbsp;Michael Livesey","doi":"10.1112/jlms.12943","DOIUrl":"https://doi.org/10.1112/jlms.12943","url":null,"abstract":"<p>We classify all 2-blocks with abelian defect groups of rank 4 up to Morita equivalence. The classification holds for blocks over a suitable discrete valuation ring as well as for those over an algebraically closed field. An application is that Broué's abelian defect group conjecture holds for all blocks under consideration here.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12943","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141182210","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Transferring compactness","authors":"Tom Benhamou,&nbsp;Jing Zhang","doi":"10.1112/jlms.12940","DOIUrl":"https://doi.org/10.1112/jlms.12940","url":null,"abstract":"<p>We demonstrate that the technology of Radin forcing can be used to transfer compactness properties at a weakly inaccessible but not strong limit cardinal to a strongly inaccessible cardinal. As an application, relative to the existence of large cardinals, we construct a model of set theory in which there is a strongly inaccessible cardinal <span></span><math>\u0000 <semantics>\u0000 <mi>κ</mi>\u0000 <annotation>$kappa$</annotation>\u0000 </semantics></math> that is <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>-<span></span><math>\u0000 <semantics>\u0000 <mi>d</mi>\u0000 <annotation>$d$</annotation>\u0000 </semantics></math>-stationary for all <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>∈</mo>\u0000 <mi>ω</mi>\u0000 </mrow>\u0000 <annotation>$nin omega$</annotation>\u0000 </semantics></math> but not weakly compact. This is in sharp contrast to the situation in the constructible universe <span></span><math>\u0000 <semantics>\u0000 <mi>L</mi>\u0000 <annotation>$L$</annotation>\u0000 </semantics></math>, where <span></span><math>\u0000 <semantics>\u0000 <mi>κ</mi>\u0000 <annotation>$kappa$</annotation>\u0000 </semantics></math> being <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(n+1)$</annotation>\u0000 </semantics></math>-<span></span><math>\u0000 <semantics>\u0000 <mi>d</mi>\u0000 <annotation>$d$</annotation>\u0000 </semantics></math>-stationary is equivalent to <span></span><math>\u0000 <semantics>\u0000 <mi>κ</mi>\u0000 <annotation>$kappa$</annotation>\u0000 </semantics></math> being <span></span><math>\u0000 <semantics>\u0000 <msubsup>\u0000 <mi>Π</mi>\u0000 <mi>n</mi>\u0000 <mn>1</mn>\u0000 </msubsup>\u0000 <annotation>$mathbf {Pi }^1_n$</annotation>\u0000 </semantics></math>-indescribable. We also show that it is consistent that there is a cardinal <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>κ</mi>\u0000 <mo>⩽</mo>\u0000 <msup>\u0000 <mn>2</mn>\u0000 <mi>ω</mi>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$kappa leqslant 2^omega$</annotation>\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12940","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141182226","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Totally deranged elements of almost simple groups and invariable generating sets","authors":"Scott Harper","doi":"10.1112/jlms.12935","DOIUrl":"https://doi.org/10.1112/jlms.12935","url":null,"abstract":"<p>By a classical theorem of Jordan, every faithful transitive action of a non-trivial finite group has a derangement (an element with no fixed points). The existence of derangements with additional properties has attracted much attention, especially for faithful primitive actions of almost simple groups. In this paper, we show that an almost simple group can have an element that is a derangement in <i>every</i> faithful primitive action, and we call these elements <i>totally deranged</i>. In fact, we classify the totally deranged elements of all almost simple groups, showing that an almost simple group <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> contains a totally deranged element only if the socle of <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> is <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>Sp</mi>\u0000 <mn>4</mn>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mn>2</mn>\u0000 <mi>f</mi>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$mathrm{Sp}_4(2^f)$</annotation>\u0000 </semantics></math> or <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>P</mi>\u0000 <msubsup>\u0000 <mi>Ω</mi>\u0000 <mi>n</mi>\u0000 <mo>+</mo>\u0000 </msubsup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>q</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$mathrm{P}Omega ^+_n(q)$</annotation>\u0000 </semantics></math> with <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>=</mo>\u0000 <msup>\u0000 <mn>2</mn>\u0000 <mi>l</mi>\u0000 </msup>\u0000 <mo>⩾</mo>\u0000 <mn>8</mn>\u0000 </mrow>\u0000 <annotation>$n=2^l geqslant 8$</annotation>\u0000 </semantics></math>. Using this, we classify the invariable generating sets of a finite simple group <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> of the form <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>{</mo>\u0000 <mi>x</mi>\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12935","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141182227","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}