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

{"title":"Hofer–Zehnder capacity of disc tangent bundles of projective spaces","authors":"Johanna Bimmermann","doi":"10.1112/jlms.12948","DOIUrl":"https://doi.org/10.1112/jlms.12948","url":null,"abstract":"<p>We compute the Hofer–Zehnder capacity of disc tangent bundles of the complex and real projective spaces of any dimension. The disc bundle is taken with respect to the Fubini–Study resp. round metric, but we can obtain explicit bounds for any other metric. In the case of the complex projective space, we also compute the Hofer–Zehnder capacity for the magnetically twisted case, where the twist is proportional to the Fubini–Study form. For arbitrary twists, we can still give explicit upper bounds.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12948","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141488421","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":"Nonfree almost finite actions for locally finite-by-virtually \u0000 \u0000 Z\u0000 ${mathbb {Z}}$\u0000 groups","authors":"Kang Li,&nbsp;Xin Ma","doi":"10.1112/jlms.12959","DOIUrl":"https://doi.org/10.1112/jlms.12959","url":null,"abstract":"<p>In this paper, we study almost finiteness and almost finiteness in measure of nonfree actions. Let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>α</mi>\u0000 <mo>:</mo>\u0000 <mi>G</mi>\u0000 <mi>↷</mi>\u0000 <mi>X</mi>\u0000 </mrow>\u0000 <annotation>$alpha:Gcurvearrowright X$</annotation>\u0000 </semantics></math> be a minimal action of a locally finite-by-virtually <span></span><math>\u0000 <semantics>\u0000 <mi>Z</mi>\u0000 <annotation>${mathbb {Z}}$</annotation>\u0000 </semantics></math> group <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> on the Cantor set <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math>. We prove that under certain assumptions, the action <span></span><math>\u0000 <semantics>\u0000 <mi>α</mi>\u0000 <annotation>$alpha$</annotation>\u0000 </semantics></math> is almost finite in measure if and only if <span></span><math>\u0000 <semantics>\u0000 <mi>α</mi>\u0000 <annotation>$alpha$</annotation>\u0000 </semantics></math> is essentially free. As an application, we obtain that any minimal topologically free action of a virtually <span></span><math>\u0000 <semantics>\u0000 <mi>Z</mi>\u0000 <annotation>${mathbb {Z}}$</annotation>\u0000 </semantics></math> group on an infinite compact metrizable space with the small boundary property is almost finite. This is the first general result, assuming only topological freeness, in this direction, and these lead to new results on uniform property <span></span><math>\u0000 <semantics>\u0000 <mi>Γ</mi>\u0000 <annotation>$Gamma$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mi>Z</mi>\u0000 <annotation>$mathcal {Z}$</annotation>\u0000 </semantics></math>-stability for their crossed product <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <annotation>$C^*$</annotation>\u0000 </semantics></math>-algebras. Some concrete examples of minimal topological free (but nonfree) subshifts are provided.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141488426","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 K-stability of \u0000 \u0000 \u0000 P\u0000 3\u0000 \u0000 $mathbb {P}^3$\u0000 blown up along a (2,3) complete intersection","authors":"Tiago Duarte Guerreiro,&nbsp;Luca Giovenzana,&nbsp;Nivedita Viswanathan","doi":"10.1112/jlms.12961","DOIUrl":"https://doi.org/10.1112/jlms.12961","url":null,"abstract":"<p>We prove K-stability of every smooth member of the Fano 3-fold family 2.15 of the Mori, Mukai and Iskovskikh classification.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12961","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141488151","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":"Hahn series and Mahler equations: Algorithmic aspects","authors":"C. Faverjon,&nbsp;J. Roques","doi":"10.1112/jlms.12945","DOIUrl":"https://doi.org/10.1112/jlms.12945","url":null,"abstract":"<p>Many articles have recently been devoted to Mahler equations, partly because of their links with other branches of mathematics such as automata theory. Hahn series (a generalization of the Puiseux series allowing arbitrary exponents of the indeterminate as long as the set that supports them is well ordered) play a central role in the theory of Mahler equations. In this paper, we address the following fundamental question: is there an algorithm to calculate the Hahn series solutions of a given linear Mahler equation? What makes this question interesting is the fact that the Hahn series appearing in this context can have complicated supports with infinitely many accumulation points. Our (positive) answer to the above question involves among other things the construction of a computable well-ordered receptacle for the supports of the potential Hahn series solutions.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141430228","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":"Corrigendum: Transcendental Brauer groups of products of CM elliptic curves","authors":"Rachel Newton","doi":"10.1112/jlms.12953","DOIUrl":"https://doi.org/10.1112/jlms.12953","url":null,"abstract":"<p>This is a corrigendum to the paper <i>Transcendental Brauer groups of products of CM elliptic curves</i>, published in (J. Lond. Math. Soc. <b>93</b> (2016), 397–419). In this note, we point out a mistake affecting the statements of Theorems 1.3, 5.2, 5.3 and Proposition 5.1 in <i>op. cit</i>., and provide a correction.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12953","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141425026","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":"Coalescence and total-variation distance of semi-infinite inverse-gamma polymers","authors":"Firas Rassoul-Agha,&nbsp;Timo Seppäläinen,&nbsp;Xiao Shen","doi":"10.1112/jlms.12955","DOIUrl":"https://doi.org/10.1112/jlms.12955","url":null,"abstract":"<p>We show that two semi-infinite positive temperature polymers coalesce on the scale predicted by KPZ (Kardar–Parisi–Zhang) universality. The two polymer paths have the same asymptotic direction and evolve in the same environment, independently until coalescence. If they start at distance <span></span><math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$k$</annotation>\u0000 </semantics></math> apart, their coalescence occurs on the scale <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>k</mi>\u0000 <mrow>\u0000 <mn>3</mn>\u0000 <mo>/</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>$k^{3/2}$</annotation>\u0000 </semantics></math>. It follows that the total variation distance of two semi-infinite polymer measures decays on this same scale. Our results are upper and lower bounds on probabilities and expectations that match, up to constant factors and occasional logarithmic corrections. Our proofs are done in the context of the solvable inverse-gamma polymer model, but without appeal to integrable probability. With minor modifications, our proofs give also bounds on transversal fluctuations of the polymer path. As the free energy of a directed polymer is a discretization of a stochastically forced viscous Hamilton–Jacobi equation, our results suggest that the hyperbolicity phenomenon of such equations obeys the KPZ exponent.</p>","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":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141326625","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 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}