Journal of Topology最新文献

{"title":"Simplicial volume and essentiality of manifolds fibered over spheres","authors":"Thorben Kastenholz,&nbsp;Jens Reinhold","doi":"10.1112/topo.12286","DOIUrl":"10.1112/topo.12286","url":null,"abstract":"<p>We study the question when a manifold that fibers over a sphere can be rationally essential, or have positive simplicial volume. More concretely, we show that mapping tori of manifolds (whose fundamental groups can be quite arbitrary) of dimension <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>n</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 <mo>⩾</mo>\u0000 <mn>7</mn>\u0000 </mrow>\u0000 <annotation>$2n +1 geqslant 7$</annotation>\u0000 </semantics></math> with non-zero simplicial volume are very common. This contrasts the case of fiber bundles over a sphere of dimension <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 <mo>⩾</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$dgeqslant 2$</annotation>\u0000 </semantics></math>: we prove that their total spaces are rationally inessential if <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 <mo>⩾</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$dgeqslant 3$</annotation>\u0000 </semantics></math>, and always have simplicial volume 0. Using a result by Dranishnikov, we also deduce a surprising property of macroscopic dimension, and we give two applications to positive scalar curvature and characteristic classes, respectively.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"16 1","pages":"192-206"},"PeriodicalIF":1.1,"publicationDate":"2023-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.12286","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41675764","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":"On the Milnor number of non-isolated singularities of holomorphic foliations and its topological invariance","authors":"Arturo Fernández-Pérez,&nbsp;Gilcione Nonato Costa,&nbsp;Rudy Rosas Bazán","doi":"10.1112/topo.12281","DOIUrl":"10.1112/topo.12281","url":null,"abstract":"<p>We define the Milnor number of a one-dimensional holomorphic foliation <math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$mathcal {F}$</annotation>\u0000 </semantics></math> as the intersection number of two holomorphic sections with respect to a compact connected component <math>\u0000 <semantics>\u0000 <mi>C</mi>\u0000 <annotation>$C$</annotation>\u0000 </semantics></math> of its singular set. Under certain conditions, we prove that the Milnor number of <math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$mathcal {F}$</annotation>\u0000 </semantics></math> on a three-dimensional manifold with respect to <math>\u0000 <semantics>\u0000 <mi>C</mi>\u0000 <annotation>$C$</annotation>\u0000 </semantics></math> is invariant by <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <annotation>$C^1$</annotation>\u0000 </semantics></math> topological equivalences.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"16 1","pages":"176-191"},"PeriodicalIF":1.1,"publicationDate":"2023-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41519115","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":"Large genus asymptotics for lengths of separating closed geodesics on random surfaces","authors":"Xin Nie,&nbsp;Yunhui Wu,&nbsp;Yuhao Xue","doi":"10.1112/topo.12276","DOIUrl":"10.1112/topo.12276","url":null,"abstract":"<p>In this paper, we investigate basic geometric quantities of a random hyperbolic surface of genus <math>\u0000 <semantics>\u0000 <mi>g</mi>\u0000 <annotation>$g$</annotation>\u0000 </semantics></math> with respect to the Weil–Petersson measure on the moduli space <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>M</mi>\u0000 <mi>g</mi>\u0000 </msub>\u0000 <annotation>$mathcal {M}_g$</annotation>\u0000 </semantics></math>. We show that as <math>\u0000 <semantics>\u0000 <mi>g</mi>\u0000 <annotation>$g$</annotation>\u0000 </semantics></math> goes to infinity, a generic surface <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>X</mi>\u0000 <mo>∈</mo>\u0000 <msub>\u0000 <mi>M</mi>\u0000 <mi>g</mi>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$Xin mathcal {M}_g$</annotation>\u0000 </semantics></math> satisfies asymptotically: \u0000\u0000 </p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"16 1","pages":"106-175"},"PeriodicalIF":1.1,"publicationDate":"2023-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49377726","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":"End-periodic homeomorphisms and volumes of mapping tori","authors":"Elizabeth Field,&nbsp;Heejoung Kim,&nbsp;Christopher Leininger,&nbsp;Marissa Loving","doi":"10.1112/topo.12277","DOIUrl":"https://doi.org/10.1112/topo.12277","url":null,"abstract":"<p>Given an 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> of a surface with finitely many ends, all accumulated by genus, the mapping torus, <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>M</mi>\u0000 <mi>f</mi>\u0000 </msub>\u0000 <annotation>$M_f$</annotation>\u0000 </semantics></math>, is the interior of a compact, irreducible, atoroidal 3-manifold <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> with incompressible boundary. Our main result is an upper bound on the infimal hyperbolic 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> in terms of the translation length of <math>\u0000 <semantics>\u0000 <mi>f</mi>\u0000 <annotation>$f$</annotation>\u0000 </semantics></math> on the pants graph of <math>\u0000 <semantics>\u0000 <mi>S</mi>\u0000 <annotation>$S$</annotation>\u0000 </semantics></math>. This builds on work of Brock and Agol in the finite-type setting. We also construct a broad class of examples of irreducible, end-periodic homeomorphisms and use them to show that our bound is asymptotically sharp.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"16 1","pages":"57-105"},"PeriodicalIF":1.1,"publicationDate":"2023-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.12277","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50122479","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":"Random subcomplexes of finite buildings, and fibering of commutator subgroups of right-angled Coxeter groups","authors":"Eduard Schesler,&nbsp;Matthew C. B. Zaremsky","doi":"10.1112/topo.12278","DOIUrl":"10.1112/topo.12278","url":null,"abstract":"<p>The main theme of this paper is higher virtual algebraic fibering properties of right-angled Coxeter groups (RACGs), with a special focus on those whose defining flag complex is a finite building. We prove for particular classes of finite buildings that their random induced subcomplexes have a number of strong properties, most prominently that they are highly connected. From this we are able to deduce that the commutator subgroup of a RACG, with defining flag complex a finite building of a certain type, admits an epimorphism to <math>\u0000 <semantics>\u0000 <mi>Z</mi>\u0000 <annotation>$mathbb {Z}$</annotation>\u0000 </semantics></math> whose kernel has strong topological finiteness properties. We additionally use our techniques to present examples where the kernel is of type <math>\u0000 <semantics>\u0000 <msub>\u0000 <mo>F</mo>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <annotation>$operatorname{F}_2$</annotation>\u0000 </semantics></math> but not <math>\u0000 <semantics>\u0000 <msub>\u0000 <mo>FP</mo>\u0000 <mn>3</mn>\u0000 </msub>\u0000 <annotation>$operatorname{FP}_3$</annotation>\u0000 </semantics></math>, and examples where the RACG is hyperbolic and the kernel is finitely generated and non-hyperbolic. The key tool we use is a generalization of an approach due to Jankiewicz–Norin–Wise involving Bestvina–Brady discrete Morse theory applied to the Davis complex of a RACG, together with some probabilistic arguments.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"16 1","pages":"20-56"},"PeriodicalIF":1.1,"publicationDate":"2023-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48971862","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":"A criterion for density of the isoperiodic leaves in rank one affine invariant orbifolds","authors":"Florent Ygouf","doi":"10.1112/topo.12279","DOIUrl":"https://doi.org/10.1112/topo.12279","url":null,"abstract":"<p>We define on any affine invariant orbifold <math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$mathcal {M}$</annotation>\u0000 </semantics></math> a foliation <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>F</mi>\u0000 <mi>M</mi>\u0000 </msup>\u0000 <annotation>$mathcal {F}^{mathcal {M}}$</annotation>\u0000 </semantics></math> that generalizes the isoperiodic foliation on strata of the moduli space of translation surfaces and study the dynamics of its leaves in the rank 1 case. We establish a criterion that ensures the density of the leaves and provide two applications of this criterion. The first one is a classification of the dynamical behavior of the leaves of <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>F</mi>\u0000 <mi>M</mi>\u0000 </msup>\u0000 <annotation>$mathcal {F}^{mathcal {M}}$</annotation>\u0000 </semantics></math> when <math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$mathcal {M}$</annotation>\u0000 </semantics></math> is a connected component of a Prym eigenform locus in genus 2 or 3 and the second provides the first examples of dense isoperiodic leaves in the stratum <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 <mo>(</mo>\u0000 <mn>2</mn>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathcal {H}(2,1,1)$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"16 1","pages":"1-19"},"PeriodicalIF":1.1,"publicationDate":"2022-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.12279","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50146539","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 criterion for density of the isoperiodic leaves in rank one affine invariant orbifolds","authors":"Florent Ygouf","doi":"10.1112/topo.12279","DOIUrl":"https://doi.org/10.1112/topo.12279","url":null,"abstract":"We define on any affine invariant orbifold M$mathcal {M}$ a foliation FM$mathcal {F}^{mathcal {M}}$ that generalizes the isoperiodic foliation on strata of the moduli space of translation surfaces and study the dynamics of its leaves in the rank 1 case. We establish a criterion that ensures the density of the leaves and provide two applications of this criterion. The first one is a classification of the dynamical behavior of the leaves of FM$mathcal {F}^{mathcal {M}}$ when M$mathcal {M}$ is a connected component of a Prym eigenform locus in genus 2 or 3 and the second provides the first examples of dense isoperiodic leaves in the stratum H(2,1,1)$mathcal {H}(2,1,1)$ .","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"16 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"63413602","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 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}