Journal of Topology最新文献

{"title":"Graphically discrete groups and rigidity","authors":"Alex Margolis,&nbsp;Sam Shepherd,&nbsp;Emily Stark,&nbsp;Daniel J. Woodhouse","doi":"10.1112/topo.70059","DOIUrl":"10.1112/topo.70059","url":null,"abstract":"<p>We introduce the notion of graphical discreteness to group theory. A finitely generated group is graphically discrete if whenever it acts geometrically on a locally finite graph, the automorphism group of the graph is compact-by-discrete. Notable examples include finitely generated nilpotent groups, most lattices in semisimple Lie groups, and irreducible nongeometric 3-manifold groups. We show graphs of groups with graphically discrete vertex groups frequently have strong rigidity properties. We prove free products of one-ended virtually torsion-free graphically discrete groups are action rigid within the class of virtually torsion-free groups. We also prove quasi-isometric rigidity for many hyperbolic graphs of groups whose vertex groups are closed hyperbolic manifold groups and whose edge groups are nonelementary quasi-convex subgroups. This includes the case of two hyperbolic 3-manifold groups amalgamated along a quasi-convex malnormal non-abelian free subgroup. We provide several additional examples of graphically discrete groups and illustrate this property is not a commensurability invariant.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"19 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146099430","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":"","authors":"","doi":"","DOIUrl":"","url":null,"abstract":"","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"19 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148084045","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 equivalence and refinements of Rasmussen's s-invariant","authors":"Nathan M. Dunfield,&nbsp;Robert Lipshitz,&nbsp;Dirk Schütz","doi":"10.1112/topo.70056","DOIUrl":"10.1112/topo.70056","url":null,"abstract":"<p>Inspired by the notions of local equivalence in monopole and Heegaard Floer homology, we introduce a version of local equivalence that combines odd Khovanov homology with equivariant even Khovanov homology into an algebraic package called a local even–odd (LEO) triple. We get a homomorphism from the smooth concordance group <span></span><math>\u0000 <semantics>\u0000 <mi>C</mi>\u0000 <annotation>$mathcal {C}$</annotation>\u0000 </semantics></math> to the resulting local equivalence group <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>C</mi>\u0000 <mi>LEO</mi>\u0000 </msub>\u0000 <annotation>$mathcal {C}_{mathit {LEO}}$</annotation>\u0000 </semantics></math> of such triples. We give several versions of the <span></span><math>\u0000 <semantics>\u0000 <mi>s</mi>\u0000 <annotation>$s$</annotation>\u0000 </semantics></math>-invariant that descend to <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>C</mi>\u0000 <mi>LEO</mi>\u0000 </msub>\u0000 <annotation>$mathcal {C}_{mathit {LEO}}$</annotation>\u0000 </semantics></math>, including one that completely determines whether the image of a knot <span></span><math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math> in <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>C</mi>\u0000 <mi>LEO</mi>\u0000 </msub>\u0000 <annotation>$mathcal {C}_{mathit {LEO}}$</annotation>\u0000 </semantics></math> is trivial. We discuss computer experiments illustrating the power of these invariants in obstructing sliceness, both statistically and for some interesting knots studied by Manolescu–Piccirillo. Along the way, we explore several variants of this local equivalence group, including one that is totally ordered.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"19 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/topo.70056","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146091153","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":"Entropy rigidity for cusped Hitchin representations","authors":"Richard Canary,&nbsp;Tengren Zhang,&nbsp;Andrew Zimmer","doi":"10.1112/topo.70064","DOIUrl":"10.1112/topo.70064","url":null,"abstract":"<p>We establish an entropy rigidity theorem for Hitchin representations of geometrically finite Fuchsian groups which generalizes a theorem of Potrie and Sambarino for Hitchin representations of closed surface groups. In the process, we introduce the class of (1,1,2)-hypertransverse groups and show for such a group that the Hausdorff dimension of its conical limit set agrees with its (first) simple root entropy, providing a common generalization of results of Bishop and Jones, for Kleinian groups, and Pozzetti, Sambarino, and Wienhard, for Anosov groups. We also introduce the theory of transverse representations of projectively visible groups as a tool for studying discrete subgroups of linear groups that are not necessarily Anosov or relatively Anosov.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"19 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/topo.70064","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146083164","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":"WDVV-based recursion for open Gromov–Witten invariants","authors":"Roi Blumberg,&nbsp;Sara B. Tukachinsky","doi":"10.1112/topo.70063","DOIUrl":"10.1112/topo.70063","url":null,"abstract":"<p>We give a computability result for open Gromov–Witten invariants based on open Witten–Dijkgraaf–Verlinde–Verlinde (WDVV) equations. This is analogous to the result of Kontsevich–Manin for closed Gromov–Witten invariants. For greater generality, we base the argument on a formal object, the Frobenius superpotential, that generalizes several different definitions of open Gromov–Witten invariants. As an application, we prove vanishing properties for open Gromov–Witten invariants on products of projective spaces.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"19 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/topo.70063","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145986976","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":"","authors":"","doi":"","DOIUrl":"","url":null,"abstract":"","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"19 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148075254","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":"","authors":"","doi":"","DOIUrl":"","url":null,"abstract":"","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"19 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148070377","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 strong Arnold chord conjecture for convex contact forms","authors":"Jungsoo Kang","doi":"10.1112/topo.70062","DOIUrl":"10.1112/topo.70062","url":null,"abstract":"<p>The original Arnold chord conjecture states that every closed Legendrian submanifold of the standard contact sphere <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>$S^{2n-1}$</annotation>\u0000 </semantics></math> admits a Reeb chord with distinct endpoints with respect to any contact form. In this paper, we prove this conjecture for contact forms induced by strictly convex embeddings into <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>$mathbb {R}^{2n}$</annotation>\u0000 </semantics></math> under the assumption that minimal periodic Reeb orbits are of Morse–Bott type. We also provide a counterexample when the convexity condition is not satisfied.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"19 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145964099","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":"Simultaneous universal circles","authors":"Michael P. Landry,&nbsp;Yair N. Minsky,&nbsp;Samuel J. Taylor","doi":"10.1112/topo.70054","DOIUrl":"10.1112/topo.70054","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <mi>φ</mi>\u0000 <annotation>$varphi$</annotation>\u0000 </semantics></math> be a pseudo-Anosov flow on a closed oriented atoroidal 3-manifold <span></span><math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>\u0000 </semantics></math>. We show that if <span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$mathcal {F}$</annotation>\u0000 </semantics></math> is any taut foliation almost transverse to <span></span><math>\u0000 <semantics>\u0000 <mi>φ</mi>\u0000 <annotation>$varphi$</annotation>\u0000 </semantics></math>, then the action of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>π</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>M</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$pi _1(M)$</annotation>\u0000 </semantics></math> on the boundary of the flow space, together with a natural collection of explicitly described monotone maps, defines a universal circle for <span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$mathcal {F}$</annotation>\u0000 </semantics></math> in the sense of Thurston and Calegari–Dunfield.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"19 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145887958","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":"","authors":"","doi":"","DOIUrl":"","url":null,"abstract":"","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"19 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148100421","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}