Journal of Topology最新文献

{"title":"Legendrian non-isotopic unit conormal bundles in high dimensions","authors":"Yukihiro Okamoto","doi":"10.1112/topo.70039","DOIUrl":"https://doi.org/10.1112/topo.70039","url":null,"abstract":"<p>For any compact connected submanifold <span></span><math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math> of <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>, let <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>Λ</mi>\u0000 <mi>K</mi>\u0000 </msub>\u0000 <annotation>$Lambda _K$</annotation>\u0000 </semantics></math> denote its unit conormal bundle, which is a Legendrian submanifold of the unit cotangent bundle of <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>. In this paper, we give examples of pairs <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>K</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>K</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(K_0,K_1)$</annotation>\u0000 </semantics></math> of compact connected submanifolds of <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> such that <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>Λ</mi>\u0000 <msub>\u0000 <mi>K</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 </msub>\u0000 <annotation>$Lambda _{K_0}$</annotation>\u0000 </semantics></math> is not Legendrian isotopic to <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>Λ</mi>\u0000 <msub>\u0000 <mi>K</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 </msub>\u0000 <annotation>$Lambda _{K_1}$</annotation>\u0000 </semantics></math>, although they cannot be distinguished by classical invariants. Here, <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>K</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <annotation>$K_1$</annotation>\u0000 </semantics></math> is","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"18 3","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/topo.70039","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037735","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":"G\u0000 $G$\u0000 -typical Witt vectors with coefficients and the norm","authors":"Thomas Read","doi":"10.1112/topo.70038","DOIUrl":"https://doi.org/10.1112/topo.70038","url":null,"abstract":"<p>For a profinite group <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> we describe an abelian group <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>W</mi>\u0000 <mi>G</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>R</mi>\u0000 <mo>;</mo>\u0000 <mi>M</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$W_G(R; M)$</annotation>\u0000 </semantics></math> of <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math>-typical Witt vectors with coefficients in an <span></span><math>\u0000 <semantics>\u0000 <mi>R</mi>\u0000 <annotation>$R$</annotation>\u0000 </semantics></math>-module <span></span><math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>\u0000 </semantics></math> (where <span></span><math>\u0000 <semantics>\u0000 <mi>R</mi>\u0000 <annotation>$R$</annotation>\u0000 </semantics></math> is a commutative ring). This simultaneously generalises the ring <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>W</mi>\u0000 <mi>G</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>R</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$W_G(R)$</annotation>\u0000 </semantics></math> of Dress and Siebeneicher and the Witt vectors with coefficients <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>W</mi>\u0000 <mo>(</mo>\u0000 <mi>R</mi>\u0000 <mo>;</mo>\u0000 <mi>M</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$W(R; M)$</annotation>\u0000 </semantics></math> of Dotto, Krause, Nikolaus and Patchkoria, both of which extend the usual Witt vectors of a ring. We use this new variant of Witt vectors to give a purely algebraic description of the zeroth equivariant stable homotopy groups of the Hill–Hopkins–Ravenel norm <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msubsup>\u0000 <mi>N</mi>\u0000 <mrow>\u0000 <mo>{</mo>\u0000 <mi>e</mi>\u0000 <mo>}</mo>\u0000 ","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"18 3","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/topo.70038","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037930","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":"Homogeneous braids are visually prime","authors":"Peter Feller,&nbsp;Lukas Lewark,&nbsp;Miguel Orbegozo Rodriguez","doi":"10.1112/topo.70040","DOIUrl":"https://doi.org/10.1112/topo.70040","url":null,"abstract":"<p>We show that closures of homogeneous braids are visually prime, addressing a question of Cromwell. The key technical tool for the proof is the following criterion concerning primeness of open books, which we consider to be of independent interest. For open books of 3-manifolds the property of having no fixed essential arcs is preserved under essential Murasugi sums with a strictly right-veering open book, if the plumbing region of the original open book veers to the left. We also provide examples of open books 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> demonstrating that primeness is not necessarily preserved under essential Murasugi sum, in fact not even under stabilizations also known as Hopf plumbings. Furthermore, we find that trefoil plumbings need not preserve primeness. In contrast, we establish that figure-eight knot plumbings do preserve primeness.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"18 3","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/topo.70040","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037940","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":"A universal finite-type invariant of knots in homology 3-spheres","authors":"Benjamin Audoux,&nbsp;Delphine Moussard","doi":"10.1112/topo.70036","DOIUrl":"https://doi.org/10.1112/topo.70036","url":null,"abstract":"<p>An essential goal in the study of finite-type invariants of some objects (knots, manifolds) is the construction of a universal finite-type invariant, universal in the sense that it contains all finite-type invariants of the given objects. Such a universal finite-type invariant is known for knots in the 3-sphere — the Kontsevich integral — and for homology 3-spheres — the Le–Murakami–Ohtsuki invariant. For knots in homology 3-spheres, an invariant constructed by Garoufalidis and Kricker as a lift of the Kontsevich integral has been considered for the last two decades as the best candidate to be a universal finite-type invariant. Although this invariant is eventually universal in restriction to knots whose Alexander polynomial is trivial, we prove here that it is not powerful enough in general. For that, we provide a refinement of its construction which produces a strictly stronger invariant, and we prove that this new invariant is a universal finite-type invariant of knots in homology 3-spheres. This provides a full diagrammatic description of the graded space of finite-type invariants of knots in homology 3-spheres.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"18 3","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/topo.70036","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145012989","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":"Rigidity of Kleinian groups via self-joinings: measure theoretic criterion","authors":"Dongryul M. Kim,&nbsp;Hee Oh","doi":"10.1112/topo.70035","DOIUrl":"https://doi.org/10.1112/topo.70035","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>,</mo>\u0000 <mi>m</mi>\u0000 <mo>⩾</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$n, mgeqslant 2$</annotation>\u0000 </semantics></math>. Let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Γ</mi>\u0000 <mo>&lt;</mo>\u0000 <msup>\u0000 <mtext>SO</mtext>\u0000 <mo>∘</mo>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$Gamma &lt;text{SO}^circ (n+1,1)$</annotation>\u0000 </semantics></math> be a Zariski dense convex cocompact subgroup and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Λ</mi>\u0000 <mo>⊂</mo>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$Lambda subset mathbb {S}^n$</annotation>\u0000 </semantics></math> be its limit set. Let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ρ</mi>\u0000 <mo>:</mo>\u0000 <mi>Γ</mi>\u0000 <mo>→</mo>\u0000 <msup>\u0000 <mtext>SO</mtext>\u0000 <mo>∘</mo>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>m</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$rho: Gamma rightarrow text{SO}^circ (m+1,1)$</annotation>\u0000 </semantics></math> be a Zariski dense convex cocompact faithful representation and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>f</mi>\u0000 <mo>:</mo>\u0000 <mi>Λ</mi>\u0000 <mo>→</mo>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mi>m</mi>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$f:Lambda rightarrow mathbb {S}^{m}$</annotation>\u0000 </semantics></math> the <span></span><math>\u0000 <semantics>\u0000 <mi>ρ</mi>\u0000 <annotation>$rho$</annotation>\u0000 </semantics></math>-boundary map. Let\u0000\u0000 </p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"18 3","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144927225","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":"The induced metric and bending lamination on the boundary of convex hyperbolic 3-manifolds","authors":"Abderrahim Mesbah","doi":"10.1112/topo.70031","DOIUrl":"https://doi.org/10.1112/topo.70031","url":null,"abstract":"&lt;p&gt;Let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;annotation&gt;$S$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be an oriented closed surface of genus at least two, and let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;M&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;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$M = S times (0,1)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Suppose that &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;h&lt;/mi&gt;\u0000 &lt;annotation&gt;$h$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is a Riemannian metric on &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;annotation&gt;$S$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; with curvature strictly greater than &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;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$-1$&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;msup&gt;\u0000 &lt;mi&gt;h&lt;/mi&gt;\u0000 &lt;mo&gt;∗&lt;/mo&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$h^{*}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is a Riemannian metric on &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;annotation&gt;$S$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; with curvature strictly less than 1, and every contractible closed geodesic with respect to &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;h&lt;/mi&gt;\u0000 &lt;mo&gt;∗&lt;/mo&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$h^{*}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; has length strictly greater than &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mi&gt;π&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$2pi$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Let &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; be a measured lamination on &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;annotation&gt;$S$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; such that every closed leaf has weight strictly less than &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;π&lt;/mi&gt;\u0000 &lt;annotation&gt;$pi$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Then, we prove the existence of a convex hyperbolic metric &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; on the interior of &lt;span&gt;&lt;/span&gt;&lt;math","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"18 3","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144915067","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":"Real topological Hochschild homology of perfectoid rings","authors":"Jens Hornbostel,&nbsp;Doosung Park","doi":"10.1112/topo.70032","DOIUrl":"https://doi.org/10.1112/topo.70032","url":null,"abstract":"<p>We refine several results of Bhatt–Morrow–Scholze on <span></span><math>\u0000 <semantics>\u0000 <mi>THH</mi>\u0000 <annotation>$mathrm{THH}$</annotation>\u0000 </semantics></math> to real topological Hochschild homology (<span></span><math>\u0000 <semantics>\u0000 <mi>THR</mi>\u0000 <annotation>$mathrm{THR}$</annotation>\u0000 </semantics></math>). In particular, we compute <span></span><math>\u0000 <semantics>\u0000 <mi>THR</mi>\u0000 <annotation>$mathrm{THR}$</annotation>\u0000 </semantics></math> of perfectoid rings. This will be useful for establishing motivic filtrations on real topological Hochschild and cyclic homology of quasisyntomic rings. We also establish a real refinement of the Hochschild–Kostant–Rosenberg theorem.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"18 3","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144832801","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":"Asymptotics of quantum \u0000 \u0000 \u0000 6\u0000 j\u0000 \u0000 $6j$\u0000 -symbols and generalized hyperbolic tetrahedra","authors":"Giulio Belletti,&nbsp;Tian Yang","doi":"10.1112/topo.70033","DOIUrl":"https://doi.org/10.1112/topo.70033","url":null,"abstract":"<p>We establish the geometry behind the quantum <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>6</mn>\u0000 <mi>j</mi>\u0000 </mrow>\u0000 <annotation>$6j$</annotation>\u0000 </semantics></math>-symbols under only the admissibility conditions as in the definition of the Turaev–Viro invariants of 3-manifolds. As a classification, we show that the 6-tuples in the quantum <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>6</mn>\u0000 <mi>j</mi>\u0000 </mrow>\u0000 <annotation>$6j$</annotation>\u0000 </semantics></math>-symbols give in a precise way to the dihedral angles of (1) a spherical tetrahedron, (2) a generalized Euclidean tetrahedron, (3) a generalized hyperbolic tetrahedron or (4) in the degenerate case the angles between four oriented straight lines in the Euclidean plane. We also show that for a large proportion of the cases, the 6-tuples always give the dihedral angles of a generalized hyperbolic tetrahedron and the exponential growth rate of the corresponding quantum <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>6</mn>\u0000 <mi>j</mi>\u0000 </mrow>\u0000 <annotation>$6j$</annotation>\u0000 </semantics></math>-symbols equals the suitably defined volume of this generalized hyperbolic tetrahedron. It is worth mentioning that the volume of a generalized hyperbolic tetrahedron can be negative, hence the corresponding sequence of the quantum <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>6</mn>\u0000 <mi>j</mi>\u0000 </mrow>\u0000 <annotation>$6j$</annotation>\u0000 </semantics></math>-symbols could decay exponentially. This is a phenomenon that has never been seen before.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"18 3","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.70033","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144782564","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":"An \u0000 \u0000 \u0000 L\u0000 ∞\u0000 \u0000 $L_infty$\u0000 structure for Legendrian contact homology","authors":"Lenhard Ng","doi":"10.1112/topo.70034","DOIUrl":"https://doi.org/10.1112/topo.70034","url":null,"abstract":"<p>For any Legendrian knot or link in <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mn>3</mn>\u0000 </msup>\u0000 <annotation>$mathbb {R}^3$</annotation>\u0000 </semantics></math>, we construct an <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>L</mi>\u0000 <mi>∞</mi>\u0000 </msub>\u0000 <annotation>$L_infty$</annotation>\u0000 </semantics></math> algebra that can be viewed as an extension of the Chekanov–Eliashberg differential graded algebra. The <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>L</mi>\u0000 <mi>∞</mi>\u0000 </msub>\u0000 <annotation>$L_infty$</annotation>\u0000 </semantics></math> structure incorporates information from rational symplectic field theory and can be formulated combinatorially. One consequence is the construction of a Poisson bracket on commutative Legendrian contact homology, and we show that the resulting Poisson algebra is an invariant of Legendrian links under isotopy.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"18 3","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144740506","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":"Counting double cosets with application to generic 3-manifolds","authors":"Suzhen Han,&nbsp;Wenyuan Yang,&nbsp;Yanqing Zou","doi":"10.1112/topo.70029","DOIUrl":"https://doi.org/10.1112/topo.70029","url":null,"abstract":"<p>We study the growth of double cosets in the class of groups with contracting elements, including relatively hyperbolic groups, CAT(0) groups and mapping class groups among others. Generalizing a recent work of Gitik and Rips about hyperbolic groups, we prove that the double coset growth of two Morse subgroups of infinite index is comparable with the orbital growth function. The same result is further obtained for a more general class of subgroups whose limit sets are proper subsets in the entire limit set of the ambient group. The limit sets under consideration are defined in a general convergence compactification, including Gromov boundary, Bowditch boundary, Thurston boundary and horofunction boundary. As an application, we confirm a conjecture of Maher that hyperbolic 3-manifolds are exponentially generic in the set of 3-manifolds built from Heegaard splitting using complexity in Teichmüller metric.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"18 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144672881","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}