Journal of Topology最新文献

Real models for the framed little n $n$ -disks operads 实际模型的框架小n$ n$ -磁盘操作

IF 1.1 2区数学

Journal of Topology Pub Date : 2025-10-09 DOI: 10.1112/topo.70042

Anton Khoroshkin, Thomas Willwacher

{"title":"Real models for the framed little \u0000 \u0000 n\u0000 $n$\u0000 -disks operads","authors":"Anton Khoroshkin, Thomas Willwacher","doi":"10.1112/topo.70042","DOIUrl":"https://doi.org/10.1112/topo.70042","url":null,"abstract":"We study the action of the orthogonal group on the little <math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>-disks operads. As an application we provide small models (over the reals) for the framed little <math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>-disks operads. It follows in particular that the framed little <math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>-disks operads are formal (over the reals) for <math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math> even and coformal for all <math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>.","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"18 4","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/topo.70042","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145248673","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}

引用次数: 0

Legendrian non-isotopic unit conormal bundles in high dimensions 高维的勒让德非同位素单位正法线束

IF 1.1 2区数学

Journal of Topology Pub Date : 2025-09-12 DOI: 10.1112/topo.70039

Yukihiro Okamoto

{"title":"Legendrian non-isotopic unit conormal bundles in high dimensions","authors":"Yukihiro Okamoto","doi":"10.1112/topo.70039","DOIUrl":"10.1112/topo.70039","url":null,"abstract":"For any compact connected submanifold <math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math> of <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 <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 <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 <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 <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 <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 <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, <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}

引用次数: 0

G $G$ -typical Witt vectors with coefficients and the norm G$ G$ -具有系数和范数的典型威特向量

IF 1.1 2区数学

Journal of Topology Pub Date : 2025-09-11 DOI: 10.1112/topo.70038

Thomas Read

{"title":"G\u0000 $G$\u0000 -typical Witt vectors with coefficients and the norm","authors":"Thomas Read","doi":"10.1112/topo.70038","DOIUrl":"10.1112/topo.70038","url":null,"abstract":"For a profinite group <math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> we describe an abelian group <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 <math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math>-typical Witt vectors with coefficients in an <math>\u0000 <semantics>\u0000 <mi>R</mi>\u0000 <annotation>$R$</annotation>\u0000 </semantics></math>-module <math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>\u0000 </semantics></math> (where <math>\u0000 <semantics>\u0000 <mi>R</mi>\u0000 <annotation>$R$</annotation>\u0000 </semantics></math> is a commutative ring). This simultaneously generalises the ring <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 <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 <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}

引用次数: 0

Homogeneous braids are visually prime 均匀的辫子在视觉上是首要的

IF 1.1 2区数学

Journal of Topology Pub Date : 2025-09-11 DOI: 10.1112/topo.70040

Peter Feller, Lukas Lewark, Miguel Orbegozo Rodriguez

引用次数: 0

A universal finite-type invariant of knots in homology 3-spheres 同调三球中结点的一般有限型不变量

IF 1.1 2区数学

Journal of Topology Pub Date : 2025-09-09 DOI: 10.1112/topo.70036

Benjamin Audoux, Delphine Moussard

{"title":"A universal finite-type invariant of knots in homology 3-spheres","authors":"Benjamin Audoux, Delphine Moussard","doi":"10.1112/topo.70036","DOIUrl":"10.1112/topo.70036","url":null,"abstract":"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.","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}

引用次数: 0

A lower bound on volumes of end-periodic mapping tori 周期末映射环面的一个下界

IF 1.1 2区数学

Journal of Topology Pub Date : 2025-09-04 DOI: 10.1112/topo.70037

Elizabeth Field, Autumn Kent, Christopher Leininger, Marissa Loving

{"title":"A lower bound on volumes of end-periodic mapping tori","authors":"Elizabeth Field, Autumn Kent, Christopher Leininger, Marissa Loving","doi":"10.1112/topo.70037","DOIUrl":"10.1112/topo.70037","url":null,"abstract":"We provide a lower bound on the volume of the compactified mapping torus of a strongly irreducible end-periodic homeomorphism <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>f</mi>\u0000 <mo>:</mo>\u0000 <mi>S</mi>\u0000 <mo>→</mo>\u0000 <mi>S</mi>\u0000 </mrow>\u0000 <annotation>$f: S rightarrow S$</annotation>\u0000 </semantics></math>. This result, together with work of Field, Kim, Leininger, and Loving [J. Topol. 16 (2023), no. 1, 57–105], shows that the volume of <math>\u0000 <semantics>\u0000 <msub>\u0000 <mover>\u0000 <mi>M</mi>\u0000 <mo>¯</mo>\u0000 </mover>\u0000 <mi>f</mi>\u0000 </msub>\u0000 <annotation>$overline{M}_f$</annotation>\u0000 </semantics></math> is comparable to the translation length of <math>\u0000 <semantics>\u0000 <mi>f</mi>\u0000 <annotation>$f$</annotation>\u0000 </semantics></math> on a connected component of the pants graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>P</mi>\u0000 <mo>(</mo>\u0000 <mi>S</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathcal {P}(S)$</annotation>\u0000 </semantics></math>, extending work of Brock [Comm. Anal. Geom. 11 (2003), no. 5, 987–999] in the finite-type setting on volumes of mapping tori of pseudo-Anosov homeomorphisms.","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"18 3","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/topo.70037","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144990690","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}

引用次数: 0

Rigidity of Kleinian groups via self-joinings: measure theoretic criterion Kleinian群的自连接刚性：测度理论准则

IF 1.1 2区数学

Journal of Topology Pub Date : 2025-09-02 DOI: 10.1112/topo.70035

Dongryul M. Kim, Hee Oh

{"title":"Rigidity of Kleinian groups via self-joinings: measure theoretic criterion","authors":"Dongryul M. Kim, Hee Oh","doi":"10.1112/topo.70035","DOIUrl":"10.1112/topo.70035","url":null,"abstract":"Let <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 <math>\u0000 <semantics>\u0000 <mrow>\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>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>$Gamma <text{SO}^circ (n+1,1)$</annotation>\u0000 </semantics></math> be a Zariski dense convex cocompact subgroup and <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 <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 <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 <math>\u0000 <semantics>\u0000 <mi>ρ</mi>\u0000 <annotation>$rho$</annotation>\u0000 </semantics></math>-boundary map. Let\u0000\u0000 ","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}

引用次数: 0

The induced metric and bending lamination on the boundary of convex hyperbolic 3-manifolds 凸双曲3-流形边界上的诱导度量和弯曲层合

IF 1.1 2区数学

Journal of Topology Pub Date : 2025-08-28 DOI: 10.1112/topo.70031

Abderrahim Mesbah

{"title":"The induced metric and bending lamination on the boundary of convex hyperbolic 3-manifolds","authors":"Abderrahim Mesbah","doi":"10.1112/topo.70031","DOIUrl":"10.1112/topo.70031","url":null,"abstract":"Let <math>\u0000 <semantics>\u0000 <mi>S</mi>\u0000 <annotation>$S$</annotation>\u0000 </semantics></math> be an oriented closed surface of genus at least two, and let <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>M</mi>\u0000 <mo>=</mo>\u0000 <mi>S</mi>\u0000 <mo>×</mo>\u0000 <mo>(</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$M = S times (0,1)$</annotation>\u0000 </semantics></math>. Suppose that <math>\u0000 <semantics>\u0000 <mi>h</mi>\u0000 <annotation>$h$</annotation>\u0000 </semantics></math> is a Riemannian metric on <math>\u0000 <semantics>\u0000 <mi>S</mi>\u0000 <annotation>$S$</annotation>\u0000 </semantics></math> with curvature strictly greater than <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$-1$</annotation>\u0000 </semantics></math>, <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>h</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <annotation>$h^{*}$</annotation>\u0000 </semantics></math> is a Riemannian metric on <math>\u0000 <semantics>\u0000 <mi>S</mi>\u0000 <annotation>$S$</annotation>\u0000 </semantics></math> with curvature strictly less than 1, and every contractible closed geodesic with respect to <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>h</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <annotation>$h^{*}$</annotation>\u0000 </semantics></math> has length strictly greater than <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>π</mi>\u0000 </mrow>\u0000 <annotation>$2pi$</annotation>\u0000 </semantics></math>. Let <math>\u0000 <semantics>\u0000 <mi>μ</mi>\u0000 <annotation>$mu$</annotation>\u0000 </semantics></math> be a measured lamination on <math>\u0000 <semantics>\u0000 <mi>S</mi>\u0000 <annotation>$S$</annotation>\u0000 </semantics></math> such that every closed leaf has weight strictly less than <math>\u0000 <semantics>\u0000 <mi>π</mi>\u0000 <annotation>$pi$</annotation>\u0000 </semantics></math>. Then, we prove the existence of a convex hyperbolic metric <math>\u0000 <semantics>\u0000 <mi>g</mi>\u0000 <annotation>$g$</annotation>\u0000 </semantics></math> on the interior of <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}

引用次数: 0

Real topological Hochschild homology of perfectoid rings 完美样环的实拓扑Hochschild同调

IF 1.1 2区数学

Journal of Topology Pub Date : 2025-08-12 DOI: 10.1112/topo.70032

Jens Hornbostel, Doosung Park

引用次数: 0

Asymptotics of quantum 6 j $6j$ -symbols and generalized hyperbolic tetrahedra 量子6j$ 6j$符号与广义双曲四面体的渐近性

IF 1.1 2区数学

Journal of Topology Pub Date : 2025-08-05 DOI: 10.1112/topo.70033

Giulio Belletti, Tian Yang

{"title":"Asymptotics of quantum \u0000 \u0000 \u0000 6\u0000 j\u0000 \u0000 $6j$\u0000 -symbols and generalized hyperbolic tetrahedra","authors":"Giulio Belletti, Tian Yang","doi":"10.1112/topo.70033","DOIUrl":"10.1112/topo.70033","url":null,"abstract":"We establish the geometry behind the quantum <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 <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 <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 <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.","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}

引用次数: 0