Journal of Topology最新文献

{"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}

{"title":"Twisted ambidexterity in equivariant homotopy theory","authors":"Bastiaan Cnossen","doi":"10.1112/topo.70083","DOIUrl":"https://doi.org/10.1112/topo.70083","url":null,"abstract":"<p>We develop the concept of twisted ambidexterity in a parametrized presentably symmetric monoidal <span></span><math>\u0000 <semantics>\u0000 <mi>∞</mi>\u0000 <annotation>$infty$</annotation>\u0000 </semantics></math>-category, which generalizes the notion of ambidexterity by Hopkins and Lurie and the Wirthmüller isomorphisms in equivariant stable homotopy theory, and is closely related to Costenoble–Waner duality. Our main result establishes the parametrized <span></span><math>\u0000 <semantics>\u0000 <mi>∞</mi>\u0000 <annotation>$infty$</annotation>\u0000 </semantics></math>-category of genuine <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math>-spectra for a compact Lie group <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> as the universal example of a presentably symmetric monoidal <span></span><math>\u0000 <semantics>\u0000 <mi>∞</mi>\u0000 <annotation>$infty$</annotation>\u0000 </semantics></math>-category parametrized over <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math>-spaces which is both stable and satisfies twisted ambidexterity for compact <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math>-spaces. We further extend this result to the settings of equivariant spectra over orbispaces and proper genuine equivariant spectra.</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.70083","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148282003","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":"Combinatorial zeta functions counting triangles","authors":"Leo Benard,&nbsp;Yann Chaubet,&nbsp;Nguyen Viet Dang,&nbsp;Thomas Schick","doi":"10.1112/topo.70075","DOIUrl":"https://doi.org/10.1112/topo.70075","url":null,"abstract":"<p>In this paper, we compute special values of certain combinatorial zeta functions counting geodesic paths in the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(n-1)$</annotation>\u0000 </semantics></math>-skeleton of a triangulation of an <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>-dimensional manifold. We show that they carry a topological meaning. As such, we recover the first Betti and <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$L^2$</annotation>\u0000 </semantics></math>-Betti numbers of compact manifolds, and the linking number of pairs of null-homologous knots in a 3-manifold. The tool to relate the two sides (counting geodesics/topological invariants) are random walks on higher dimensional skeleta of the triangulation.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"19 2","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.70075","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148238103","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":"Exotic periodic phenomena in the cohomology of the moduli stack of one-dimensional formal group laws","authors":"Dan Isaksen,&nbsp;Hana Jia Kong,&nbsp;Guchuan Li,&nbsp;Yangyang Ruan,&nbsp;Heyi Zhu","doi":"10.1112/topo.70082","DOIUrl":"https://doi.org/10.1112/topo.70082","url":null,"abstract":"<p>We describe some periodic structure in the cohomology of the moduli stack of one-dimensional formal group laws, also known as the <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>E</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <annotation>$E_2$</annotation>\u0000 </semantics></math>-page of the classical Adams–Novikov spectral sequence. This structure is distinct from the familiar <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>v</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <annotation>$v_n$</annotation>\u0000 </semantics></math>-periodicities, and it displays interesting number-theoretic properties. Our techniques involve the <span></span><math>\u0000 <semantics>\u0000 <mi>C</mi>\u0000 <annotation>$mathbb {C}$</annotation>\u0000 </semantics></math>-motivic Adams spectral sequence, and we obtain analogous periodic structure in <span></span><math>\u0000 <semantics>\u0000 <mi>C</mi>\u0000 <annotation>$mathbb {C}$</annotation>\u0000 </semantics></math>-motivic stable homotopy.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"19 2","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148174098","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":"Thurston norm for coherent right-angled Artin groups via \u0000 \u0000 \u0000 L\u0000 2\u0000 \u0000 $L^2$\u0000 -invariants","authors":"Monika Kudlinska","doi":"10.1112/topo.70079","DOIUrl":"https://doi.org/10.1112/topo.70079","url":null,"abstract":"&lt;p&gt;We define a new notion of splitting complexity for a group &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; along a non-trivial integral character &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ϕ&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mo&gt;;&lt;/mo&gt;\u0000 &lt;mi&gt;Z&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$phi in H^1(G; mathbb {Z})$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. If &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; is a one-ended coherent right-angled Artin group, we show that the splitting complexity along an epimorphism &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ϕ&lt;/mi&gt;\u0000 &lt;mo&gt;:&lt;/mo&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mo&gt;→&lt;/mo&gt;\u0000 &lt;mi&gt;Z&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$phi colon G rightarrow mathbb {Z}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; equals the &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$L^2$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-Euler characteristic of the kernel of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;ϕ&lt;/mi&gt;\u0000 &lt;annotation&gt;$phi$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. This allows us to define a Thurston-type semi-norm &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;∥&lt;/mo&gt;\u0000 &lt;mo&gt;·&lt;/mo&gt;\u0000 &lt;mo&gt;∥&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mi&gt;T&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;:&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mo&gt;;&lt;/mo&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;→&lt;/mo&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$Vert cdot Vert _T colon H^1(G; mathbb {R}) rightarrow mathbb {R}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/mat","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"19 2","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.70079","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148174100","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 search for alternating surgeries","authors":"Kenneth L. Baker,&nbsp;Marc Kegel,&nbsp;Duncan McCoy","doi":"10.1112/topo.70081","DOIUrl":"https://doi.org/10.1112/topo.70081","url":null,"abstract":"<p>Surgery on a knot 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> is said to be an alternating surgery if it yields the double branched cover of an alternating link. The main theoretical contribution is to show that the set of alternating surgery slopes is algorithmically computable and to establish several structural results. Furthermore, we calculate the set of alternating surgery slopes for many examples of knots, including all hyperbolic knots in the SnapPy census. These examples exhibit several interesting phenomena including strongly invertible knots with a unique alternating surgery and asymmetric knots with two alternating surgery slopes. We also establish upper bounds on the set of alternating surgeries, showing that an alternating surgery slope on a hyperbolic knot satisfies <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>|</mo>\u0000 <mi>p</mi>\u0000 <mo>/</mo>\u0000 <mi>q</mi>\u0000 <mo>|</mo>\u0000 <mo>⩽</mo>\u0000 <mn>3</mn>\u0000 <mi>g</mi>\u0000 <mo>(</mo>\u0000 <mi>K</mi>\u0000 <mo>)</mo>\u0000 <mo>+</mo>\u0000 <mn>4</mn>\u0000 </mrow>\u0000 <annotation>$|p/q|leqslant 3g(K)+4$</annotation>\u0000 </semantics></math>. Notably, this bound applies to lens space surgeries, thereby strengthening the known genus bounds from the conjecture of Goda and Teragaito.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"19 2","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148173708","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":"Bounds on saddle connections for flat spheres","authors":"Kai Fu,&nbsp;Guillaume Tahar","doi":"10.1112/topo.70076","DOIUrl":"https://doi.org/10.1112/topo.70076","url":null,"abstract":"<p>We consider a flat metric with conical singularities on the sphere. Under the assumption that no partial sum of angle defects is equal to <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>π</mi>\u0000 </mrow>\u0000 <annotation>$2pi$</annotation>\u0000 </semantics></math>, we draw on the geometry of immersed disks to obtain an explicit upper bound on the number of saddle connections with at most <span></span><math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$k$</annotation>\u0000 </semantics></math> self-intersections. Additionally, we establish an upper bound on their lengths for a surface with a normalized area. Finally, we apply these bounds to the counting of singular trajectories in irrational polygonal billiards.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"19 2","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148167108","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}

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