Journal of Topology最新文献

{"title":"Isotopy versus equivariant isotopy in dimensions 3 and higher","authors":"Trent Lucas","doi":"10.1112/topo.70106","DOIUrl":"https://doi.org/10.1112/topo.70106","url":null,"abstract":"<p>Given a finite group action on a smooth manifold, we study the following question: if two equivariant diffeomorphisms are isotopic, must they be equivariantly isotopic? Birman–Hilden and Maclachlan–Harvey proved the answer is “yes” for most surfaces. By contrast, we give a general criterion in higher dimensions under which there are many equivariant diffeomorphisms that are isotopic but not equivariantly isotopic. Examples satisfying this criterion include branched covers of split links and “stabilized” branched covers. We prove the result by constructing an invariant valued in the homology of a certain infinite cover of the manifold. We give applications to outer automorphism groups of free products and to group actions on manifolds which fiber over the circle.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"19 4","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149177279","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":"On Poincaré surgery","authors":"John R. Klein","doi":"10.1112/topo.70103","DOIUrl":"https://doi.org/10.1112/topo.70103","url":null,"abstract":"<p>We exhibit a homotopy-theoretic proof of the fundamental theorem of Poincaré surgery in the simply connected case. We also deduce the Poincaré transversality exact sequence.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"19 4","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149177283","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 mod 2 Seiberg–Witten invariants of spin structures and spin families","authors":"David Baraglia","doi":"10.1112/topo.70101","DOIUrl":"https://doi.org/10.1112/topo.70101","url":null,"abstract":"<p>We completely determine the mod 2 Seiberg–Witten invariants for any spin structure on any closed, oriented, smooth 4-manifold <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math>. Our computation confirms the validity of the simple-type conjecture mod 2 for spin structures. Our proof also works for families of spin 4-manifolds and thus computes the mod 2 Seiberg–Witten invariants for spin families. The proof of our main result uses <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>P</mi>\u0000 <mi>i</mi>\u0000 <mi>n</mi>\u0000 <mo>(</mo>\u0000 <mn>2</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$Pin(2)$</annotation>\u0000 </semantics></math>-symmetry to define an enhancement of the mod 2 Seiberg–Witten invariants. We prove a connected sum formula for the enhanced invariant using localisation in equivariant cohomology. Unlike the usual Seiberg–Witten invariant, the enhanced invariant does not vanish on taking connected sums and by exploiting this property, we are able to compute the enhanced invariant.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"19 4","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.70101","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149177284","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":"Proper affine deformations of positive representations","authors":"Jean-Philippe Burelle,&nbsp;Neža Žager Korenjak","doi":"10.1112/topo.70102","DOIUrl":"https://doi.org/10.1112/topo.70102","url":null,"abstract":"<p>We define, for every positive Anosov representation of a nonabelian free group into <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>2</mn>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathrm{SO}(2n,2n-1)$</annotation>\u0000 </semantics></math>, a family of <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mrow>\u0000 <mn>4</mn>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>$mathbb {R}^{4n-1}$</annotation>\u0000 </semantics></math>-valued cocycles which induce proper affine actions on <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mrow>\u0000 <mn>4</mn>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>$mathbb {R}^{4n-1}$</annotation>\u0000 </semantics></math>. We construct fundamental domains in <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mrow>\u0000 <mn>4</mn>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>$mathbb {R}^{4n-1}$</annotation>\u0000 </semantics></math> bounded by generalized crooked planes for these affine actions, and deduce that the quotient manifolds are homeomorphic to handlebodies.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"19 4","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.70102","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149177278","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":"Simple groups and complements of smooth surfaces in simply connected 4-manifolds","authors":"Sam Hughes,&nbsp;Daniel Ruberman","doi":"10.1112/topo.70098","DOIUrl":"10.1112/topo.70098","url":null,"abstract":"<p>For each integer <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math> we construct an oriented closed simply connected 4-manifold <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> admitting a smoothly embedded closed connected surface <span></span><math>\u0000 <semantics>\u0000 <mi>Σ</mi>\u0000 <annotation>$Sigma$</annotation>\u0000 </semantics></math> of self-intersection number <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math> such that the complement of the surface has non-trivial fundamental group. This answers a question of Kronheimer in Kirby's 1997 problem list. The proof combines a topological construction with homological properties of simple groups such as Thompson's group <span></span><math>\u0000 <semantics>\u0000 <mi>V</mi>\u0000 <annotation>$V$</annotation>\u0000 </semantics></math> and certain sporadic finite simple groups.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"19 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.70098","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148932737","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":"Finite abelian group actions on weakly Lefschetz cohomologically symplectic manifolds","authors":"Ignasi Mundet i Riera","doi":"10.1112/topo.70095","DOIUrl":"10.1112/topo.70095","url":null,"abstract":"&lt;p&gt;We study continuous finite abelian group actions on &lt;i&gt;weakly Lefschetz cohomologically symplectic&lt;/i&gt; (WLS) manifolds, a collection of topological manifolds that includes all compact connected Kaehler manifolds. We prove that for any WLS manifold &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;annotation&gt;$X$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, there exists a number &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;annotation&gt;$C$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; such that, for any integer &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;mi&gt;C&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$mgeqslant C$&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;msup&gt;\u0000 &lt;mrow&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;mi&gt;m&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$({mathbb {Z}}/m)^k$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; acts freely on &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;annotation&gt;$X$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, then &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mo&gt;∑&lt;/mo&gt;\u0000 &lt;mi&gt;j&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;b&lt;/mi&gt;\u0000 &lt;mi&gt;j&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;;&lt;/mo&gt;\u0000 &lt;mi&gt;Q&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;⩾&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$sum _j b_j(X;{mathbb {Q}})geqslant 2^k$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. We also prove a structure theorem for effective actions on WLS manifolds of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&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;mi&gt;p&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$({mathbb {Z}}/p)^r$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, where &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"19 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.70095","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148932736","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":"Invariant splitting principles for the Lipshitz–Ozsváth–Thurston correspondence","authors":"Gary Guth,&nbsp;Sungkyung Kang","doi":"10.1112/topo.70097","DOIUrl":"10.1112/topo.70097","url":null,"abstract":"<p>We prove that the Lipshitz–Ozsváth–Thurston correspondence between extended type D structures of knot complements and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>F</mi>\u0000 <mo>[</mo>\u0000 <mi>U</mi>\u0000 <mo>,</mo>\u0000 <mi>V</mi>\u0000 <mo>]</mo>\u0000 <mo>/</mo>\u0000 <mo>(</mo>\u0000 <mi>UV</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathbb{F}[U,V]/(textit{UV})$</annotation>\u0000 </semantics></math> knot Floer complexes can be arranged so that <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>ι</mi>\u0000 <mi>K</mi>\u0000 </msub>\u0000 <annotation>${iota}_{K}$</annotation>\u0000 </semantics></math>-invariant splittings of knot Floer chain complexes correspond to <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>ι</mi>\u0000 <mrow>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mn>3</mn>\u0000 </msup>\u0000 <mo>∖</mo>\u0000 <mi>K</mi>\u0000 </mrow>\u0000 </msub>\u0000 <annotation>${iota}_{{S}^{3}setminus K}$</annotation>\u0000 </semantics></math>-invariant splittings of bordered Floer homology of knot complements. This provides a novel way to compute the involutive knot Floer homology of satellites from that of their companions. As a topological application, we show that our results can be applied to construct infinitely many examples of exotic pairs of contractible 4-manifolds which remain exotic after one stabilization. Along the way, we also establish first-order naturality of bordered Floer homology.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"19 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.70097","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148894637","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":"Simple homotopy theory for Fukaya categories","authors":"Yonghwan Kim","doi":"10.1112/topo.70099","DOIUrl":"https://doi.org/10.1112/topo.70099","url":null,"abstract":"<p>We develop a categorical framework for simple homotopy theory in Fukaya categories, based on the fundamental group of the ambient symplectic manifold. When the first Chern class vanishes, we show that any isomorphism in the Fukaya category of a Weinstein manifold has trivial Whitehead torsion. As an application, we prove that any pair of closed connected Lagrangians that are isomorphic in the Fukaya category of such a Weinstein manifolds are simple homotopy equivalent, provided one of the Lagrangians is homotopy equivalent to the ambient symplectic manifold and their fundamental groups are isomorphic.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"19 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.70099","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148849110","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":"Pinwheels in symplectic rational and ruled surfaces and non-squeezing of rational homology balls","authors":"Nikolas Adaloglou,&nbsp;Johannes Hauber","doi":"10.1112/topo.70094","DOIUrl":"https://doi.org/10.1112/topo.70094","url":null,"abstract":"&lt;p&gt;We use almost toric fibrations and the symplectic rational blow-up to determine when certain Lagrangian pinwheels, which we call &lt;i&gt;liminal&lt;/i&gt;, embed in symplectic rational and ruled surfaces. The case of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$L_{2,1}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-pinwheels, namely Lagrangian &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;P&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$mathbb {R}P^2{rm s}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, answers a question of Kronheimer in the negative, exhibiting a symplectic non-spin four-manifold that does not carry a Lagrangian &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;P&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$mathbb {R}P^2$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. In addition, we provide applications to symplectic embeddings of rational homology balls. In particular, we generalize Gromov's classical non-squeezing theorem by proving that a &lt;i&gt;rational homology ball&lt;/i&gt; &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;B&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$B_{n,1}(1)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; embeds into the &lt;i&gt;rational homology cylinder&lt;/i&gt; &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;B&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$B_","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"19 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.70094","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148848732","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":"Picard groups of quotient ring spectra","authors":"Ishan Levy,&nbsp;Guchuan Li,&nbsp;Ningchuan Zhang","doi":"10.1112/topo.70093","DOIUrl":"https://doi.org/10.1112/topo.70093","url":null,"abstract":"<p>We develop tools to study Picard groups of quotients of ring spectra by a finitely generated ideal, which we use to show that <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Pic</mi>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>E</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <mo>/</mo>\u0000 <mi>I</mi>\u0000 <mo>)</mo>\u0000 <mo>=</mo>\u0000 <mi>Z</mi>\u0000 <mo>/</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$mathrm{Pic}(mathrm{E}_n/I) = mathbb {Z}/2$</annotation>\u0000 </semantics></math>, where <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>E</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <annotation>$mathrm{E}_n$</annotation>\u0000 </semantics></math> is a Lubin–Tate theory and <span></span><math>\u0000 <semantics>\u0000 <mi>I</mi>\u0000 <annotation>$I$</annotation>\u0000 </semantics></math> is an ideal generated by suitable powers of a regular sequence. We apply this to obtain spectral sequences computing Picard groups of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>K</mi>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathrm{K}(n)$</annotation>\u0000 </semantics></math>-local generalized Moore algebras, and make some preliminary computations including the height 1 case.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"19 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148784794","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}