Journal of Topology最新文献

{"title":"Effective length-projection bounds for hyperbolic 3-manifolds diffeomorphic to \u0000 \u0000 \u0000 S\u0000 ×\u0000 R\u0000 \u0000 $Stimes mathbb {R}$","authors":"Gabriele Viaggi","doi":"10.1112/topo.70096","DOIUrl":"https://doi.org/10.1112/topo.70096","url":null,"abstract":"<p>We give a formula with explicit constants relating the subsurface projection <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>d</mi>\u0000 <mi>Y</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>ν</mi>\u0000 <mo>−</mo>\u0000 </msup>\u0000 <mo>,</mo>\u0000 <msup>\u0000 <mi>ν</mi>\u0000 <mo>+</mo>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$d_Y(nu ^-,nu ^+)$</annotation>\u0000 </semantics></math> of the end invariants <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>ν</mi>\u0000 <mo>−</mo>\u0000 </msup>\u0000 <mo>,</mo>\u0000 <msup>\u0000 <mi>ν</mi>\u0000 <mo>+</mo>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$nu ^-,nu ^+$</annotation>\u0000 </semantics></math> of a hyperbolic 3-manifold <span></span><math>\u0000 <semantics>\u0000 <mi>Q</mi>\u0000 <annotation>$Q$</annotation>\u0000 </semantics></math> diffeomorphic to <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>S</mi>\u0000 <mo>×</mo>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 <annotation>$Stimes mathbb {R}$</annotation>\u0000 </semantics></math> and the length of the geodesic representative in <span></span><math>\u0000 <semantics>\u0000 <mi>Q</mi>\u0000 <annotation>$Q$</annotation>\u0000 </semantics></math> of the multicurve <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>∂</mi>\u0000 <mi>Y</mi>\u0000 </mrow>\u0000 <annotation>$partial Y$</annotation>\u0000 </semantics></math>. This makes effective and computable the large projections versus short curves relation proved by Minsky. We give an application to closed hyperbolic 3-manifolds fibering over the circle providing a geometric analog of the uniform projection bound in fibered faces of Minsky and Taylor.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"19 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.70096","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148784668","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":"Higher representation stability for ordered configuration spaces","authors":"Quoc P. Ho","doi":"10.1112/topo.70092","DOIUrl":"https://doi.org/10.1112/topo.70092","url":null,"abstract":"<p>Using factorization homology with coefficients in twisted commutative algebras (TCAs), we prove two flavors of higher representation stability for the cohomology of (generalized) configuration spaces of a scheme/topological space <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math>. First, we provide an iterative procedure to study higher representation stability using actions coming from the cohomology of <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> and prove that all the modules involved are finitely generated over the corresponding TCAs. More quantitatively, we compute explicit bounds for the derived indecomposables in the sense of Galatius–Kupers–Randal–Williams. Second, when certain <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>C</mi>\u0000 <mi>∞</mi>\u0000 </msub>\u0000 <annotation>${C}_{infty}$</annotation>\u0000 </semantics></math>-operations on the cohomology of <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> vanish, we prove that the cohomology of its configuration spaces forms a free module over a TCA built out of the configuration spaces of the affine space. This generalizes a result of Church–Ellenberg–Farb on the freeness of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>FI</mo>\u0000 </mrow>\u0000 <annotation>$operatorname{mathrm{FI}}$</annotation>\u0000 </semantics></math>-modules arising from the cohomology of configuration spaces of open manifolds and, moreover, resolves the various conjectures of Miller–Wilson under these conditions.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"19 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.70092","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148616638","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":"Exodromy beyond conicality","authors":"Peter J. Haine,&nbsp;Mauro Porta,&nbsp;Jean-Baptiste Teyssier","doi":"10.1112/topo.70091","DOIUrl":"https://doi.org/10.1112/topo.70091","url":null,"abstract":"<p>We show that compact subanalytic stratified spaces and algebraic stratifications of real varieties have finite exit-path <span></span><math>\u0000 <semantics>\u0000 <mi>∞</mi>\u0000 <annotation>$infty $</annotation>\u0000 </semantics></math>-categories, refining the classical theorems of Lefschetz–Whitehead, Łojasiewicz, and Hironaka on the finiteness of the underlying homotopy types of these spaces. These stratifications are typically not conical; hence, we cannot rely on the currently available exodromy equivalence between constructible sheaves on a stratified space, which requires conicality as a fundamental hypothesis. Building on ideas of Clausen and Jansen, we study the class of <i>exodromic</i> stratified spaces, for which the conclusion of the exodromy theorem holds. We prove two new fundamental properties of this class of stratified spaces: coarsenings of exodromic stratifications are exodromic, and every morphism between exodromic stratified spaces induces a functor between the associated exit path <span></span><math>\u0000 <semantics>\u0000 <mi>∞</mi>\u0000 <annotation>$infty $</annotation>\u0000 </semantics></math>-categories. As a consequence, we produce many new examples of exodromic stratified spaces, including: coarsenings of conical stratifications, locally finite subanalytic stratifications of real analytic spaces, and algebraic stratifications of real varieties. Our proofs are at the generality of stratified <span></span><math>\u0000 <semantics>\u0000 <mi>∞</mi>\u0000 <annotation>$infty $</annotation>\u0000 </semantics></math>-topoi, hence apply to even more general situations such as stratified topological stacks. In a subsequent paper, we use the previously mentioned finiteness results to construct derived moduli stacks of constructible and perverse sheaves.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"19 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148615893","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":"Localization sequences for logarithmic topological cyclic homology","authors":"John Rognes,&nbsp;Steffen Sagave,&nbsp;Christian Schlichtkrull","doi":"10.1112/topo.70090","DOIUrl":"https://doi.org/10.1112/topo.70090","url":null,"abstract":"<p>We introduce the notion of an <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>E</mi>\u0000 <mi>k</mi>\u0000 </msub>\u0000 <annotation>$mathbb {E}_k$</annotation>\u0000 </semantics></math>-ring with prelogarithmic structure, define logarithmic topological Hochschild homology and logarithmic topological cyclic homology in this context, and establish localization sequences for these theories. Our approach is based on Thom <span></span><math>\u0000 <semantics>\u0000 <mi>R</mi>\u0000 <annotation>$R$</annotation>\u0000 </semantics></math>-algebras. It extends and strengthens our earlier work on the subject in several regards. Our examples include the fraction field of topological <span></span><math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math>-theory, the existence of which was suggested by calculations by Ausoni and the first author. To illustrate the computational accessibility of log <span></span><math>\u0000 <semantics>\u0000 <mi>THH</mi>\u0000 <annotation>$mathrm{THH}$</annotation>\u0000 </semantics></math> and log <span></span><math>\u0000 <semantics>\u0000 <mi>TC</mi>\u0000 <annotation>$mathrm{TC}$</annotation>\u0000 </semantics></math>, we determine these for non-negative even periodic sphere spectra, with their canonical prelogarithmic structures.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"19 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.70090","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148615211","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":"Surface subgroups for cocompact lattices of isometries of \u0000 \u0000 \u0000 H\u0000 \u0000 2\u0000 n\u0000 \u0000 \u0000 $mathbb {H}^{2n}$","authors":"Jeremy Kahn,&nbsp;Zhenghao Rao","doi":"10.1112/topo.70089","DOIUrl":"https://doi.org/10.1112/topo.70089","url":null,"abstract":"<p>We prove the existence of surface subgroups within any cocompact lattice <span></span><math>\u0000 <semantics>\u0000 <mi>Γ</mi>\u0000 <annotation>$Gamma$</annotation>\u0000 </semantics></math> in <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>SO</mi>\u0000 <mo>(</mo>\u0000 <mn>2</mn>\u0000 <mi>n</mi>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathrm{SO}(2n,1)$</annotation>\u0000 </semantics></math> for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>⩾</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$ngeqslant 2$</annotation>\u0000 </semantics></math>. This result addresses the cases missing from the work of Hamenstädt in 2015, who constructed surface subgroups in cocompact lattices for all other rank-1 simple Lie groups of noncompact type.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"19 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.70089","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148467375","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":"Torus decomposition and foliation detected slopes","authors":"Qingfeng Lyu","doi":"10.1112/topo.70088","DOIUrl":"https://doi.org/10.1112/topo.70088","url":null,"abstract":"&lt;p&gt;Let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$M_1$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$M_2$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be knot manifolds and &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;msub&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;msub&gt;\u0000 &lt;mo&gt;∪&lt;/mo&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$M=M_1cup _f M_2$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be the closed manifold obtained by gluing up &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$M_1$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$M_2$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; via &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;mo&gt;:&lt;/mo&gt;\u0000 &lt;mi&gt;∂&lt;/mi&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mover&gt;\u0000 &lt;mo&gt;→&lt;/mo&gt;\u0000 &lt;mo&gt;≅&lt;/mo&gt;\u0000 &lt;/mover&gt;\u0000 &lt;mi&gt;∂&lt;/mi&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$f:partial M_1xrightarrow {cong } partial M_2$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. We show that if &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;annotation&gt;$M$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; admits a co-oriented taut foliation, then &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;annotation&gt;$f$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; identifies some CTF-detected rational boundary slopes of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$M_1$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"19 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148466913","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":"Free semigroups of large critical exponent","authors":"Aleksander Skenderi","doi":"10.1112/topo.70087","DOIUrl":"https://doi.org/10.1112/topo.70087","url":null,"abstract":"<p>For a convergence group equipped with an expanding coarse-cocycle, we construct finitely generated free subsemigroups, which we call <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Bishop</mi>\u0000 <mo>−</mo>\u0000 <mo>−</mo>\u0000 <mi>Jonessemigroups</mi>\u0000 </mrow>\u0000 <annotation>$textit{Bishop--Jones semigroups}$</annotation>\u0000 </semantics></math>, of critical exponent arbitrarily close to but strictly less than the critical exponent of the ambient group. As an application, we show that for any nonelementary transverse subgroup <span></span><math>\u0000 <semantics>\u0000 <mi>Γ</mi>\u0000 <annotation>$Gamma$</annotation>\u0000 </semantics></math> of a semisimple Lie group <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math>, there exist finitely generated free Anosov subsemigroups in the sense of Kassel–Potrie of critical exponent arbitrarily close to but strictly less than that of the ambient transverse group. Furthermore, we show that these semigroups admit quasi-isometric embeddings into the symmetric space <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> of <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> with certain additional coarse-geometric properties.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"19 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.70087","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148466604","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":"Classification of closed conformally flat Lorentzian manifolds with unipotent holonomy","authors":"Rachel Lee,&nbsp;Karin Melnick","doi":"10.1112/topo.70085","DOIUrl":"https://doi.org/10.1112/topo.70085","url":null,"abstract":"<p>We classify closed, conformally flat Lorentzian manifolds of dimension <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>⩾</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$n geqslant 3$</annotation>\u0000 </semantics></math> with unipotent holonomy in PO(2,n). They are all Kleinian and fall into four different geometric types according to the intersection of the image of the developing map with a holonomy-invariant isotropic flag. They are homeomorphic to <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 <mo>×</mo>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$S^{n-1} times S^1$</annotation>\u0000 </semantics></math> or to a nilmanifold of degree at most three, up to a finite cover. We classify those admitting an essential conformal flow; these fall into two geometric types, both homeomorphic to <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 <mo>×</mo>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$S^{n-1} times S^1$</annotation>\u0000 </semantics></math> up to finite cover.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"19 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148357996","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 \u0000 \u0000 \u0000 C\u0000 2\u0000 \u0000 ${C_2}$\u0000 -equivariant ordinary cohomology of \u0000 \u0000 \u0000 B\u0000 \u0000 T\u0000 2\u0000 \u0000 \u0000 $BT^2$","authors":"Steven R. Costenoble,&nbsp;Thomas Hudson","doi":"10.1112/topo.70084","DOIUrl":"https://doi.org/10.1112/topo.70084","url":null,"abstract":"<p>We calculate the ordinary <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>C</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <annotation>${C_2}$</annotation>\u0000 </semantics></math>-cohomology of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>B</mi>\u0000 <msup>\u0000 <mi>T</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$BT^2$</annotation>\u0000 </semantics></math> with Burnside ring coefficients, using an extended grading that allows us to capture a more natural set of generators. We discuss how this cohomology is related to that of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>B</mi>\u0000 <msup>\u0000 <mi>T</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$BT^1$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>B</mi>\u0000 <mi>U</mi>\u0000 <mo>(</mo>\u0000 <mn>2</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$BU(2)$</annotation>\u0000 </semantics></math>, calculated previously, both relationships being more complicated than in the nonequivariant case.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"19 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148282123","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 quasi-redirecting boundary","authors":"Yulan Qing,&nbsp;Kasra Rafi","doi":"10.1112/topo.70080","DOIUrl":"https://doi.org/10.1112/topo.70080","url":null,"abstract":"<p>We generalize the notion of Gromov boundary to a larger class of metric spaces beyond Gromov hyperbolic spaces. Points in this boundary are classes of quasi-geodesic rays and the space is equipped with a topology that is naturally invariant under quasi-isometries. It turns out that this boundary is compatible with other notions of boundary in many ways; it contains the sublinearly Morse boundary as a topological subspace and it matches the Bowditch boundary of relative hyperbolic spaces when the peripheral subgroups have no intrinsic hyperbolicity. We also give a complete description of the boundary of the Croke–Kleiner group where the quasi-redirecting boundary reveals a new class of QI-invariant, Morse-like quasi-geodesics.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"19 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.70080","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148282002","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}