Journal of Topology最新文献

{"title":"The correspondence induced on the pillowcase by the earring tangle","authors":"Guillem Cazassus,&nbsp;Christopher Herald,&nbsp;Paul Kirk,&nbsp;Artem Kotelskiy","doi":"10.1112/topo.12272","DOIUrl":"10.1112/topo.12272","url":null,"abstract":"<p>The earring tangle consists of four strands <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>4</mn>\u0000 <mtext>pt</mtext>\u0000 <mo>×</mo>\u0000 <mi>I</mi>\u0000 <mo>⊂</mo>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mo>×</mo>\u0000 <mi>I</mi>\u0000 </mrow>\u0000 <annotation>$4text{pt} times I subset S^2 times I$</annotation>\u0000 </semantics></math> and one meridian around one of the strands. Equipping this tangle with a nontrivial <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>S</mi>\u0000 <mi>O</mi>\u0000 <mo>(</mo>\u0000 <mn>3</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$SO(3)$</annotation>\u0000 </semantics></math> bundle, we show that its traceless <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>S</mi>\u0000 <mi>U</mi>\u0000 <mo>(</mo>\u0000 <mn>2</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$SU(2)$</annotation>\u0000 </semantics></math> flat moduli space is topologically a smooth genus three surface. We also show that the restriction map from this surface to the traceless flat moduli space of the boundary of the earring tangle is a particular Lagrangian immersion into the product of two pillowcases. The latter computation suggests that figure eight bubbling — a subtle degeneration phenomenon predicted by Bottman and Wehrheim — appears in the context of traceless character varieties.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"15 4","pages":"2472-2543"},"PeriodicalIF":1.1,"publicationDate":"2022-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47353465","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":"Homotopy functoriality for Khovanov spectra","authors":"Tyler Lawson,&nbsp;Robert Lipshitz,&nbsp;Sucharit Sarkar","doi":"10.1112/topo.12274","DOIUrl":"10.1112/topo.12274","url":null,"abstract":"<p>We prove that the Khovanov spectra associated to links and tangles are functorial up to homotopy and sign.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"15 4","pages":"2426-2471"},"PeriodicalIF":1.1,"publicationDate":"2022-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45475595","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":"Heegaard genus and complexity of fibered knots","authors":"Mustafa Cengiz","doi":"10.1112/topo.12268","DOIUrl":"10.1112/topo.12268","url":null,"abstract":"<p>We prove that if a fibered knot <math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math> with genus greater than 1 in a three-manifold <math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>\u0000 </semantics></math> has a sufficiently complicated monodromy, then <math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math> induces a minimal genus Heegaard splitting <math>\u0000 <semantics>\u0000 <mi>P</mi>\u0000 <annotation>$P$</annotation>\u0000 </semantics></math> that is unique up to isotopy, and small genus Heegaard splittings of <math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>\u0000 </semantics></math> are stabilizations of <math>\u0000 <semantics>\u0000 <mi>P</mi>\u0000 <annotation>$P$</annotation>\u0000 </semantics></math>. We provide a complexity bound in terms of the Heegaard genus of <math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>\u0000 </semantics></math>. We also provide global complexity bounds for fibered knots in the three-sphere and lens spaces.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"15 4","pages":"2389-2425"},"PeriodicalIF":1.1,"publicationDate":"2022-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42863430","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":"Infinitely many virtual geometric triangulations","authors":"David Futer,&nbsp;Emily Hamilton,&nbsp;Neil R. Hoffman","doi":"10.1112/topo.12271","DOIUrl":"10.1112/topo.12271","url":null,"abstract":"<p>We prove that every cusped hyperbolic 3-manifold has a finite cover admitting infinitely many geometric ideal triangulations. Furthermore, every long Dehn filling of one cusp in this cover admits infinitely many geometric ideal triangulations. This cover is constructed in several stages, using results about separability of peripheral subgroups and their double cosets, in addition to a new conjugacy separability theorem that may be of independent interest. The infinite sequence of geometric triangulations is supported in a geometric submanifold associated to one cusp, and can be organized into an infinite trivalent tree of Pachner moves.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"15 4","pages":"2352-2388"},"PeriodicalIF":1.1,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42935185","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":"Thickness and relative hyperbolicity for graphs of multicurves","authors":"Jacob Russell,&nbsp;Kate M. Vokes","doi":"10.1112/topo.12270","DOIUrl":"10.1112/topo.12270","url":null,"abstract":"<p>We prove that any graph of multicurves satisfying certain natural properties is either hyperbolic, relatively hyperbolic, or thick. Further, this geometric characterization is determined by the set of subsurfaces that intersect every vertex of the graph. This extends previously established results for the pants graph and the separating curve graph to a broad family of graphs associated to surfaces.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"15 4","pages":"2317-2351"},"PeriodicalIF":1.1,"publicationDate":"2022-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47972858","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":"Decompositions of the stable module \u0000 \u0000 ∞\u0000 $infty$\u0000 -category","authors":"Joshua Hunt","doi":"10.1112/topo.12269","DOIUrl":"10.1112/topo.12269","url":null,"abstract":"<p>We show that the stable module <math>\u0000 <semantics>\u0000 <mi>∞</mi>\u0000 <annotation>$infty$</annotation>\u0000 </semantics></math>-category of a finite group <math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> decomposes in three different ways as a limit of the stable module <math>\u0000 <semantics>\u0000 <mi>∞</mi>\u0000 <annotation>$infty$</annotation>\u0000 </semantics></math>-categories of certain subgroups of <math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math>. Analogously to Dwyer's terminology for homology decompositions, we call these the centraliser, normaliser, and subgroup decompositions. We construct centraliser and normaliser decompositions and extend the subgroup decomposition (constructed by Mathew) to more collections of subgroups. The key step in the proof is extending the stable module <math>\u0000 <semantics>\u0000 <mi>∞</mi>\u0000 <annotation>$infty$</annotation>\u0000 </semantics></math>-category to be defined for any <math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math>-space, then showing that this extension only depends on the <math>\u0000 <semantics>\u0000 <mi>S</mi>\u0000 <annotation>$S$</annotation>\u0000 </semantics></math>-equivariant homotopy type of a <math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math>-space. The methods used are not specific to the stable module <math>\u0000 <semantics>\u0000 <mi>∞</mi>\u0000 <annotation>$infty$</annotation>\u0000 </semantics></math>-category, so may also be applicable in other settings where an <math>\u0000 <semantics>\u0000 <mi>∞</mi>\u0000 <annotation>$infty$</annotation>\u0000 </semantics></math>-category depends functorially on <math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"15 4","pages":"2298-2316"},"PeriodicalIF":1.1,"publicationDate":"2022-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71493568","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":"Étale cohomology, purity and formality with torsion coefficients","authors":"Joana Cirici,&nbsp;Geoffroy Horel","doi":"10.1112/topo.12273","DOIUrl":"10.1112/topo.12273","url":null,"abstract":"<p>We use Galois group actions on étale cohomology to prove results of formality for dg-operads and dg-algebras with torsion coefficients. Our theory applies, among other related objects, to the dg-operad of singular chains of the operad of little disks and to the dg-algebra of singular cochains of the configuration space of points in the complex space. The formality that we obtain is only up to a certain degree, which depends on the cardinality of the field of coefficients.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"15 4","pages":"2270-2297"},"PeriodicalIF":1.1,"publicationDate":"2022-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47960006","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":"Symplectic hats","authors":"John B. Etnyre,&nbsp;Marco Golla","doi":"10.1112/topo.12258","DOIUrl":"10.1112/topo.12258","url":null,"abstract":"<p>We study relative symplectic cobordisms between contact submanifolds, and in particular relative symplectic cobordisms to the empty set, that we call hats. While we make some observations in higher dimensions, we focus on the case of transverse knots in the standard 3-sphere, and hats in blow-ups of the (punctured) complex projective planes. We apply the construction to give constraints on the algebraic topology of fillings of double covers of the 3-sphere branched over certain transverse quasipositive knots.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"15 4","pages":"2216-2269"},"PeriodicalIF":1.1,"publicationDate":"2022-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/topo.12258","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47383736","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":"Homological stability for Iwahori–Hecke algebras","authors":"Richard Hepworth","doi":"10.1112/topo.12262","DOIUrl":"10.1112/topo.12262","url":null,"abstract":"<p>We show that the Iwahori–Hecke algebras <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>H</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <annotation>$mathcal {H}_n$</annotation>\u0000 </semantics></math> of type <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>A</mi>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msub>\u0000 <annotation>$A_{n-1}$</annotation>\u0000 </semantics></math> satisfy homological stability, where homology is interpreted as an appropriate Tor group. Our result precisely recovers Nakaoka's homological stability result for the symmetric groups in the case that the defining parameter is equal to 1. We believe that this paper, and our joint work with Boyd on Temperley–Lieb algebras, are the first time that the techniques of homological stability have been applied to algebras that are not group algebras.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"15 4","pages":"2174-2215"},"PeriodicalIF":1.1,"publicationDate":"2022-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/topo.12262","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44124588","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 Picard group of the universal moduli stack of principal bundles on pointed smooth curves","authors":"Roberto Fringuelli,&nbsp;Filippo Viviani","doi":"10.1112/topo.12257","DOIUrl":"10.1112/topo.12257","url":null,"abstract":"<p>For any smooth connected linear algebraic group <math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> over an algebraically closed field <math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$k$</annotation>\u0000 </semantics></math>, we describe the Picard group of the universal moduli stack of principal <math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math>-bundles over pointed smooth <math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$k$</annotation>\u0000 </semantics></math>-projective curves.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"15 4","pages":"2065-2142"},"PeriodicalIF":1.1,"publicationDate":"2022-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41376353","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}