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

{"title":"Symbolic dynamics for nonuniformly hyperbolic flows in high dimension","authors":"Yuri Lima,&nbsp;Juan Carlos Mongez,&nbsp;João Paulo Nascimento","doi":"10.1112/jlms.70731","DOIUrl":"https://doi.org/10.1112/jlms.70731","url":null,"abstract":"<p>We construct symbolic dynamics for flows with positive speed in any dimension: for each <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>χ</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$chi &gt;0$</annotation>\u0000 </semantics></math>, we code a set that has full measure for every invariant probability measure that is <span></span><math>\u0000 <semantics>\u0000 <mi>χ</mi>\u0000 <annotation>$chi$</annotation>\u0000 </semantics></math>-hyperbolic. In particular, the coded set contains all hyperbolic periodic orbits with Lyapunov exponents outside of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>[</mo>\u0000 <mo>−</mo>\u0000 <mi>χ</mi>\u0000 <mo>,</mo>\u0000 <mi>χ</mi>\u0000 <mo>]</mo>\u0000 </mrow>\u0000 <annotation>$[-chi,chi]$</annotation>\u0000 </semantics></math>. This extends the recent work of Buzzi, Crovisier, and Lima for three-dimensional flows with positive speed [Buzzi et al., Adv. Math. <b>479</b> (2025), 110410]. As an application, we code homoclinic classes of measures by suspensions of irreducible countable Markov shifts, and prove that each such class has at most one probability measure that maximizes the entropy.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 4","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149206079","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":"Homogeneity in Coxeter groups and split crystallographic groups","authors":"Simon André,&nbsp;Gianluca Paolini","doi":"10.1112/jlms.70730","DOIUrl":"https://doi.org/10.1112/jlms.70730","url":null,"abstract":"<p>We prove that affine Coxeter groups, even hyperbolic Coxeter groups and one-ended hyperbolic Coxeter groups, are homogeneous in the sense of model theory. More generally, we prove that many (Gromov) hyperbolic groups generated by torsion elements are homogeneous. In contrast, we construct split crystallographic groups that are not homogeneous, and hyperbolic (in fact, virtually free) Coxeter groups that are not homogeneous (or, to be more precise, not <span></span><math>\u0000 <semantics>\u0000 <mi>EAE</mi>\u0000 <annotation>$mathrm{EAE}$</annotation>\u0000 </semantics></math>-homogeneous). We also prove that, on the other hand, irreducible split crystallographic groups and torsion-generated hyperbolic groups are almost homogeneous. We also prove that finitely generated abelian-by-finite groups are homogeneous if and only if they are profinitely homogeneous, that is, any tuple of words from the group is profinitely rigid. We use this to deduce that affine Coxeter groups are profinitely homogeneous, a result of independent interest in the profinite context.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 4","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149205597","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":"Parametrised functor calculus: Excision, spheres, and semiadditivity","authors":"Kaif Hilman,&nbsp;Sil Linskens","doi":"10.1112/jlms.70722","DOIUrl":"https://doi.org/10.1112/jlms.70722","url":null,"abstract":"<p>We lay down the foundations of a theory of <i>parametrised functor calculus</i>, generalising parts of the functor calculus of Goodwillie. We introduce the notion of excisable posets and develop a theory of excisive approximations in this context. As an application, we introduce two different excisable posets when parametrising over an atomic orbital category. By comparing the notions of excisiveness for these two posets, we relate the invertibility of certain spheres to Nardin's notion of parametrised semiadditivity, generalising Wirthmüller's classical result in equivariant homotopy theory for finite groups.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 4","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70722","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149205312","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":"Universal properties of Delannoy categories","authors":"Kevin Coulembier,&nbsp;Nate Harman,&nbsp;Andrew Snowden","doi":"10.1112/jlms.70733","DOIUrl":"https://doi.org/10.1112/jlms.70733","url":null,"abstract":"&lt;p&gt;Recently, Harman and Snowden introduced a new symmetric tensor category &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;munder&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;P&lt;/mi&gt;\u0000 &lt;mi&gt;e&lt;/mi&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;mi&gt;m&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;̲&lt;/mo&gt;\u0000 &lt;/munder&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;μ&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$operatorname{underline{Perm}}(G, mu)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; associated with an oligomorphic group &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;annotation&gt;$G$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; with a measure &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;μ&lt;/mi&gt;\u0000 &lt;annotation&gt;$mu$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. When &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;annotation&gt;$G$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is the group of order-preserving self-bijections of the real line there are four such measures, and the resulting tensor categories are called the Delannoy categories. The first Delannoy category is semisimple, and was studied in detail by Harman, Snowden, and Snyder. We give universal properties for all four Delannoy categories in terms of ordered étale algebras. As a consequence, we show that the second and third Delannoy categories admit at least two local abelian envelopes, and the fourth admits at least four. We also prove a coarser universal property for &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;munder&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;P&lt;/mi&gt;\u0000 &lt;mi&gt;e&lt;/mi&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;mi&gt;m&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;̲&lt;/mo&gt;\u0000 &lt;/munder&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;μ&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$operatorname{underline{Perm}}(G, mu)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; for a general oligomorphic group &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;annotation&gt;$","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 4","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70733","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149146560","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":"Bordered Floer homology, handlebody detection, and compressing diffeomorphisms","authors":"Akram Alishahi,&nbsp;Robert Lipshitz","doi":"10.1112/jlms.70721","DOIUrl":"https://doi.org/10.1112/jlms.70721","url":null,"abstract":"<p>We show that, up to connected sums with integer homology <span></span><math>\u0000 <semantics>\u0000 <mi>L</mi>\u0000 <annotation>$L$</annotation>\u0000 </semantics></math>-spaces, bordered Floer homology detects handlebodies, as well as whether a mapping class extends over a given handlebody or compression body. Using this, we combine ideas of Casson–Long with the theory of train tracks to give an algorithm using bordered Floer homology to detect whether a mapping class extends over any compression body.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 4","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70721","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149146198","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":"Theta classes: Generalized topological recursion, integrability, and \u0000 \u0000 W\u0000 $mathcal {W}$\u0000 -constraints","authors":"Vincent Bouchard,&nbsp;Nitin Kumar Chidambaram,&nbsp;Alessandro Giacchetto,&nbsp;Sergey Shadrin","doi":"10.1112/jlms.70728","DOIUrl":"https://doi.org/10.1112/jlms.70728","url":null,"abstract":"&lt;p&gt;We study the intersection theory of the &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;Θ&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$Theta ^{r,s}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-classes, where &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;mo&gt;⩾&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$r geqslant 2$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;⩽&lt;/mo&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;mo&gt;⩽&lt;/mo&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$1 leqslant s leqslant r-1$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, which are cohomological field theories obtained as the top degrees of Chiodo classes. We show that the recently introduced generalized topological recursion on the &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$(r,s)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; spectral curves computes the descendant integrals of the &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;Θ&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$Theta ^{r,s}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-classes. As a consequence, we deduce that the descendant potential of the &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;Θ&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$Theta ^{r,s}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-classes is a tau function of the &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;annotation&gt;$r$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-KdV hierarchy, generalizing the Brézin–Gross–Witten tau function (the special case &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$r=2$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 4","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149146199","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":"Characterizations of Hardy spaces on tube domains over polyhedral cones","authors":"Zunwei Fu,&nbsp;Loukas Grafakos,&nbsp;Wei Wang,&nbsp;Qingyan Wu","doi":"10.1112/jlms.70727","DOIUrl":"https://doi.org/10.1112/jlms.70727","url":null,"abstract":"<p>This paper is devoted to the equivalence of various characterizations of holomorphic <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <annotation>$H^1$</annotation>\u0000 </semantics></math> Hardy spaces on tube domains over polyhedral cones. We establish a new iterated Poisson integral formula that reproduces holomorphic functions on such domains. However, this formula shows that holomorphic <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <annotation>$H^1$</annotation>\u0000 </semantics></math> functions have boundary values in a new type of Hardy space of real variables on their Shilov boundaries <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <annotation>$mathbb {R}^n$</annotation>\u0000 </semantics></math>, which cannot be treated by standard multiparameter harmonic analysis. We overcome this difficulty by developing techniques suitably adapted to this setting. Using the iterated Poisson integral as our approximation to the identity and employing a lifting technique, we introduce various notions of multiparameter analysis adapted to tube domains, such as twisted rectangles, new nontangential approach regions, nontangential maximal functions, and Littlewood–Paley-type functions. All these notions exhibit new geometric features associated with polyhedral cones and involve hidden parameters, as in the flag setting. We develop the necessary multiparameter tools to investigate these new Hardy spaces. In particular, we apply these tools to obtain equivalent characterizations of the holomorphic <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <annotation>$H^1$</annotation>\u0000 </semantics></math> Hardy spaces on tube domains in terms of nontangential maximal, Lusin–Littlewood–Paley area, and Littlewood–Paley <span></span><math>\u0000 <semantics>\u0000 <mi>g</mi>\u0000 <annotation>$g$</annotation>\u0000 </semantics></math>-functions.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 4","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149146027","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":"Sharp restriction estimates for some degenerate higher codimensional quadratic surfaces","authors":"Zhenbin Cao,&nbsp;Changxing Miao,&nbsp;Yixuan Pang","doi":"10.1112/jlms.70735","DOIUrl":"https://doi.org/10.1112/jlms.70735","url":null,"abstract":"<p>The Fourier restriction conjecture is a fundamental problem in harmonic analysis. In this paper, we investigate restriction estimates for degenerate higher codimensional quadratic surfaces and obtain sharp results for some types of degenerate cases. A major obstacle in establishing sharp restriction estimates is the failure of rescaling invariance, which is crucial for induction on scale to be effective. Motivated by the work of Guo and Oh (2022), we introduce a method, building on an iterative variant of the broad–narrow analysis, that does not heavily rely on induction on scale. To obtain suitable transversality conditions for this analysis and to derive desirable bounds for the broad part, we define a generalized notion of Jacobian, and establish its structural properties. These properties are proved using tools and techniques from both algebra and graph theory.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 4","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70735","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149145946","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":"The hypergraph isomorphism game, Hopf algebras, and Galois extensions","authors":"Georgios Baziotis,&nbsp;Alexandros Chatzinikolaou,&nbsp;Gage Hoefer","doi":"10.1112/jlms.70725","DOIUrl":"https://doi.org/10.1112/jlms.70725","url":null,"abstract":"<p>We develop an algebraic and operational framework for quantum isomorphisms of hypergraphs, using tools from compact quantum group theory. We introduce a new synchronous version of the hypergraph isomorphism game whose game algebra uniformly encodes multiple notions of quantum isomorphisms of hypergraphs. We show that there exist hypergraphs that are quantum isomorphic but not classically isomorphic. For graphs, we show that the <span></span><math>\u0000 <semantics>\u0000 <mo>∗</mo>\u0000 <annotation>$*$</annotation>\u0000 </semantics></math>-algebra of the hypergraph isomorphism game is a quotient of the <span></span><math>\u0000 <semantics>\u0000 <mo>∗</mo>\u0000 <annotation>$*$</annotation>\u0000 </semantics></math>-algebra of the graph isomorphism game. We further prove that the hypergraph game algebra forms a bi-Galois extension over the quantum automorphism groups of the underlying hypergraphs. This allows us to deduce that the algebraic notion of a quantum isomorphism of hypergraphs coincides with the operational one coming from the existence of perfect quantum strategies. Viewing games themselves as hypergraphs, we analyze isomorphisms and the transfer of strategies within this setting. Finally, we construct a <span></span><math>\u0000 <semantics>\u0000 <mo>∗</mo>\u0000 <annotation>$*$</annotation>\u0000 </semantics></math>-algebra whose representation theory characterizes distinct classes of quantum isomorphisms between nonlocal games.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 4","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149145945","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":"Optimal bounds for the Kobayashi distance near \u0000 \u0000 \u0000 C\u0000 2\u0000 \u0000 $mathcal {C}^2$\u0000 -smooth boundary points","authors":"Nikolai Nikolov,&nbsp;Pascal J. Thomas","doi":"10.1112/jlms.70732","DOIUrl":"https://doi.org/10.1112/jlms.70732","url":null,"abstract":"<p>It is shown that the optimal upper and lower bounds for the Kobayashi distance near <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mo>,</mo>\u0000 <mi>α</mi>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>$mathcal {C}^{2,alpha }$</annotation>\u0000 </semantics></math>-smooth strongly pseudoconvex boundary points obtained in Kosiński, Nikolov, and Ökten [Adv. Math. <b>478</b> (2025), 110388] remain true in the general <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$mathcal {C}^2$</annotation>\u0000 </semantics></math>-smooth strongly pseudoconvex setting. In fact, the upper bound is extended to the general <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>$mathcal {C}^{1,1}$</annotation>\u0000 </semantics></math>-smooth case. We also give upper and lower bounds for the Kobayashi distance near non-semipositive boundary points.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 4","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70732","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149145794","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}