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Journal of Homotopy and Related Structures最新文献

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On the RO(Q)-graded coefficients of Eilenberg–MacLane spectra Eilenberg-MacLane光谱的RO(Q)梯度系数
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2022-10-05 DOI: 10.1007/s40062-022-00314-x
Igor Sikora
{"title":"On the RO(Q)-graded coefficients of Eilenberg–MacLane spectra","authors":"Igor Sikora","doi":"10.1007/s40062-022-00314-x","DOIUrl":"10.1007/s40062-022-00314-x","url":null,"abstract":"<div><p>Let <i>Q</i> denote the cyclic group of order two. Using the Tate diagram we compute the <i>RO</i>(<i>Q</i>)-graded coefficients of Eilenberg–MacLane <i>Q</i>-spectra and describe their structure as modules over the coefficients of the Eilenberg–MacLane spectrum of the Burnside Mackey functor. If the underlying Mackey functor is a Green functor, we also obtain the multiplicative structure on the <i>RO</i>(<i>Q</i>)-graded coefficients.</p></div>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"17 4","pages":"525 - 568"},"PeriodicalIF":0.5,"publicationDate":"2022-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40062-022-00314-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4227394","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On families of nilpotent subgroups and associated coset posets 幂零子群的族及相关的陪集集
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2022-09-14 DOI: 10.1007/s40062-022-00315-w
Simon Gritschacher, Bernardo Villarreal
{"title":"On families of nilpotent subgroups and associated coset posets","authors":"Simon Gritschacher,&nbsp;Bernardo Villarreal","doi":"10.1007/s40062-022-00315-w","DOIUrl":"10.1007/s40062-022-00315-w","url":null,"abstract":"<div><p>We study some properties of the coset poset associated with the family of subgroups of class <span>(le 2)</span> of a nilpotent group of class <span>(le 3)</span>. We prove that under certain assumptions on the group the coset poset is simply-connected if and only if the group is 2-Engel, and 2-connected if and only if the group is nilpotent of class 2 or less. We determine the homotopy type of the coset poset for the group of <span>(4times 4)</span> upper unitriangular matrices over <span>(mathbb {F}_p)</span>, and for the Burnside groups of exponent 3.</p></div>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"17 4","pages":"493 - 509"},"PeriodicalIF":0.5,"publicationDate":"2022-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4591877","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Computations of relative topological coHochschild homology 相对拓扑coHochschild同调的计算
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2022-08-05 DOI: 10.1007/s40062-022-00312-z
Sarah Klanderman
{"title":"Computations of relative topological coHochschild homology","authors":"Sarah Klanderman","doi":"10.1007/s40062-022-00312-z","DOIUrl":"10.1007/s40062-022-00312-z","url":null,"abstract":"<div><p>Hess and Shipley defined an invariant of coalgebra spectra called topological coHochschild homology, and Bohmann–Gerhardt–Høgenhaven–Shipley–Ziegenhagen developed a coBökstedt spectral sequence to compute the homology of <span>(mathrm {coTHH})</span> for coalgebras over the sphere spectrum. We construct a relative coBökstedt spectral sequence to study <span>(mathrm {coTHH})</span> of coalgebra spectra over any commutative ring spectrum <i>R</i>. Further, we use algebraic structures in this spectral sequence to complete some calculations of the homotopy groups of relative topological coHochschild homology.</p></div>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"17 3","pages":"393 - 417"},"PeriodicalIF":0.5,"publicationDate":"2022-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4200876","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Smashing localizations in equivariant stable homotopy 等变稳定同伦中的粉碎局域化
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2022-07-15 DOI: 10.1007/s40062-022-00310-1
Christian Carrick
{"title":"Smashing localizations in equivariant stable homotopy","authors":"Christian Carrick","doi":"10.1007/s40062-022-00310-1","DOIUrl":"10.1007/s40062-022-00310-1","url":null,"abstract":"<div><p>We study how smashing Bousfield localizations behave under various equivariant functors. We show that the analogs of the smash product and chromatic convergence theorems for the Real Johnson–Wilson theories <span>(E_{mathbb {R}}(n))</span> hold only after Borel completion. We establish analogous results for the <span>(C_{2^n})</span>-equivariant Johnson–Wilson theories constructed by Beaudry, Hill, Shi, and Zeng. We show that induced localizations upgrade the available norms for an <span>(N_infty )</span>-algebra, and we determine which new norms appear. Finally, we explore generalizations of our results on smashing localizations in the context of a quasi-Galois extension of <span>(E_infty )</span>-rings.</p></div>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"17 3","pages":"355 - 392"},"PeriodicalIF":0.5,"publicationDate":"2022-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40062-022-00310-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4614379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
An equivalence of profinite completions 无限完井的等价
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2022-07-06 DOI: 10.1007/s40062-022-00308-9
Chang-Yeon Chough
{"title":"An equivalence of profinite completions","authors":"Chang-Yeon Chough","doi":"10.1007/s40062-022-00308-9","DOIUrl":"10.1007/s40062-022-00308-9","url":null,"abstract":"<div><p>The goal of this paper is to establish an equivalence of profinite completions of pro-spaces in model category theory and in <span>(infty )</span>-category theory. As an application, we show that the author’s comparison theorem for algebro-geometric objects in the setting of model categories recovers that of David Carchedi in the setting of <span>(infty )</span>-categories.</p></div>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"17 3","pages":"297 - 307"},"PeriodicalIF":0.5,"publicationDate":"2022-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40062-022-00308-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4253284","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Rational stabilization and maximal ideal spaces of commutative Banach algebras 交换Banach代数的有理稳定与极大理想空间
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2022-07-01 DOI: 10.1007/s40062-022-00309-8
Kazuhiro Kawamura
{"title":"Rational stabilization and maximal ideal spaces of commutative Banach algebras","authors":"Kazuhiro Kawamura","doi":"10.1007/s40062-022-00309-8","DOIUrl":"10.1007/s40062-022-00309-8","url":null,"abstract":"<div><p>For a unital commutative Banach algebra <i>A</i> and its closed ideal <i>I</i>, we study the relative Čech cohomology of the pair <span>((mathrm {Max}(A),mathrm {Max}(A/I)))</span> of maximal ideal spaces and show a relative version of the main theorem of Lupton et al. (Trans Amer Math Soc 361:267–296, 2009): <span>(check{mathrm {H}}^{j}(mathrm {Max}(A),mathrm {Max}(A/I));{mathbb {Q}}) cong pi _{2n-j-1}(Lc_{n}(I))_{{mathbb {Q}}})</span> for <span>(j &lt; 2n-1)</span>, where <span>(Lc_{n}(I))</span> refers to the space of last columns. We then study the rational cohomological dimension <span>(mathrm {cdim}_{mathbb Q}mathrm {Max}(A))</span> for a unital commutative Banach algebra and prove an embedding theorem: if <i>A</i> is a unital commutative semi-simple regular Banach algebra such that <span>(mathrm {Max}(A))</span> is metrizable and <span>(mathrm {cdim}_{{mathbb {Q}}}mathrm {Max}(A) le m)</span>, then (i) the rational homotopy group <span>(pi _{k}(GL_{n}(A))_{{mathbb {Q}}})</span> is stabilized if <span>(n ge lceil (m+k+1)/2rceil )</span> and (ii) there exists a compact metrizable space <span>(X_A)</span> with <span>(dim X_{A} le m)</span> such that <i>A</i> is embedded into the commutative <span>(C^*)</span>-algebra <span>(C(X_{A}))</span> such that <span>(pi _{k}(GL_{n}(C(X_{A}))))</span> is rationally isomorphic to <span>(pi _{k}(GL_{n}(A)))</span> for each <span>(kge 1)</span> and <span>(pi _{k}(GL_{n}(C(X_{A})))</span> is stabilized for <span>(n ge lceil (m+k+1)/2 rceil )</span>. The main technical ingredient is a modified version of a classical theorem of Davie (Proc Lond Math Soc 23:31–52, 1971).</p></div>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"17 3","pages":"263 - 295"},"PeriodicalIF":0.5,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40062-022-00309-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4031270","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sheaves via augmentations of Legendrian surfaces 通过勒让德曲面的增广得到的轴
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2021-10-09 DOI: 10.1007/s40062-021-00292-6
Dan Rutherford, Michael Sullivan
{"title":"Sheaves via augmentations of Legendrian surfaces","authors":"Dan Rutherford,&nbsp;Michael Sullivan","doi":"10.1007/s40062-021-00292-6","DOIUrl":"10.1007/s40062-021-00292-6","url":null,"abstract":"<div><p>Given an augmentation for a Legendrian surface in a 1-jet space, <span>(Lambda subset J^1(M))</span>, we explicitly construct an object, <span>(mathcal {F} in mathbf {Sh}^bullet _{Lambda }(Mtimes mathbb {R}, mathbb {K}))</span>, of the (derived) category from Shende, Treumann and Zaslow (Invent Math <b>207</b>(3), 1031–1133 (2017)) of constructible sheaves on <span>(Mtimes mathbb {R})</span> with singular support determined by <span>(Lambda )</span>. In the construction, we introduce a simplicial Legendrian DGA (differential graded algebra) for Legendrian submanifolds in 1-jet spaces that, based on Rutherford and Sullivan (Cellular Legendrian contact homology for surfaces, Part I, arXiv:1608.02984.) Rutherford and Sullivan (Internat J Math 30(7):135, 2019) Rutherford and Sullivan (Internat J Math 30(7):111, 2019), is equivalent to the Legendrian contact homology DGA in the case of Legendrian surfaces. In addition, we extend the approach of Shende, Treumann and Zaslow (Invent Math <b>207</b>(3), 1031–1133 (2017)) for 1-dimensional Legendrian knots to obtain a combinatorial model for sheaves in <span>(mathbf {Sh}^bullet _{Lambda }(Mtimes mathbb {R}, mathbb {K}))</span> in the 2-dimensional case.</p></div>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"16 4","pages":"703 - 752"},"PeriodicalIF":0.5,"publicationDate":"2021-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4400089","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 10
Equivariant formal group laws and complex-oriented spectra over primary cyclic groups: elliptic curves, Barsotti–Tate groups, and other examples 初等循环群上的等变形式群定律和复取向谱:椭圆曲线，Barsotti-Tate群和其他例子
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2021-09-27 DOI: 10.1007/s40062-021-00291-7
Po Hu, Igor Kriz, Petr Somberg
{"title":"Equivariant formal group laws and complex-oriented spectra over primary cyclic groups: elliptic curves, Barsotti–Tate groups, and other examples","authors":"Po Hu,&nbsp;Igor Kriz,&nbsp;Petr Somberg","doi":"10.1007/s40062-021-00291-7","DOIUrl":"10.1007/s40062-021-00291-7","url":null,"abstract":"<div><p>We explicitly construct and investigate a number of examples of <span>({mathbb {Z}}/p^r)</span>-equivariant formal group laws and complex-oriented spectra, including those coming from elliptic curves and <i>p</i>-divisible groups, as well as some other related examples.</p></div>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"16 4","pages":"635 - 665"},"PeriodicalIF":0.5,"publicationDate":"2021-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40062-021-00291-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4041307","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Higher order Toda brackets 高阶Toda括号
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2021-07-27 DOI: 10.1007/s40062-021-00285-5
Aziz Kharoof
{"title":"Higher order Toda brackets","authors":"Aziz Kharoof","doi":"10.1007/s40062-021-00285-5","DOIUrl":"10.1007/s40062-021-00285-5","url":null,"abstract":"<div><p>We describe two ways to define higher order Toda brackets in a pointed simplicial model category <span>({mathcal {D}})</span>: one is a recursive definition using model categorical constructions, and the second uses the associated simplicial enrichment. We show that these two definitions agree, by providing a third, diagrammatic, description of the Toda bracket, and explain how it serves as the obstruction to rectifying a certain homotopy-commutative diagram in <span>({mathcal {D}})</span>.</p></div>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"16 3","pages":"451 - 486"},"PeriodicalIF":0.5,"publicationDate":"2021-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-021-00285-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4615394","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Cantor–Schröder–Bernstein Theorem for (infty )-groupoids （infty）-群胚的Cantor–Schröder–Bernstein定理
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2021-06-28 DOI: 10.1007/s40062-021-00284-6
Martín Hötzel Escardó
{"title":"The Cantor–Schröder–Bernstein Theorem for (infty )-groupoids","authors":"Martín Hötzel Escardó","doi":"10.1007/s40062-021-00284-6","DOIUrl":"10.1007/s40062-021-00284-6","url":null,"abstract":"<div><p>We show that the Cantor–Schröder–Bernstein Theorem for homotopy types, or <span>(infty )</span>-groupoids, holds in the following form: For any two types, if each one is embedded into the other, then they are equivalent. The argument is developed in the language of homotopy type theory, or Voevodsky’s univalent foundations (HoTT/UF), and requires classical logic. It follows that the theorem holds in any boolean <span>(infty )</span>-topos.</p></div>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"16 3","pages":"363 - 366"},"PeriodicalIF":0.5,"publicationDate":"2021-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-021-00284-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5064254","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
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