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Journal of Homotopy and Related Structures最新文献

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On the real cycle class map for singular varieties 关于奇异变量的实循环类映射
IF 0.7 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2025-04-21 DOI: 10.1007/s40062-025-00369-6
Fangzhou Jin, Heng Xie
{"title":"On the real cycle class map for singular varieties","authors":"Fangzhou Jin,&nbsp;Heng Xie","doi":"10.1007/s40062-025-00369-6","DOIUrl":"10.1007/s40062-025-00369-6","url":null,"abstract":"<div><p>We investigate the real cycle class map for singular varieties. We introduce an analog of Borel–Moore homology for algebraic varieties over the real numbers, which is defined via the hypercohomology of the Gersten–Witt complex associated with schemes possessing a dualizing complex. We show that the hypercohomology of this complex is isomorphic to the classical Borel–Moore homology for quasi-projective varieties over the real numbers.</p></div>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"20 2","pages":"293 - 321"},"PeriodicalIF":0.7,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40062-025-00369-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143925691","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
Localisations and completions of nilpotent G-spaces 幂零g空间的局部化与补全
IF 0.7 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2025-04-11 DOI: 10.1007/s40062-025-00371-y
Andrew Ronan
{"title":"Localisations and completions of nilpotent G-spaces","authors":"Andrew Ronan","doi":"10.1007/s40062-025-00371-y","DOIUrl":"10.1007/s40062-025-00371-y","url":null,"abstract":"<div><p>We develop the theory of nilpotent <i>G</i>-spaces and their localisations, for <i>G</i> a compact Lie group, via reduction to the non-equivariant case using Bousfield localisation. One point of interest in the equivariant setting is that we can choose to localise or complete at different sets of primes at different fixed point spaces—and the theory works out just as well provided that you invert more primes at <span>(K le G)</span> than at <span>(H le G)</span>, whenever <i>K</i> is subconjugate to <i>H</i> in <i>G</i>. We also develop the theory in an unbased context, allowing us to extend the theory to <i>G</i>-spaces which are not <i>G</i>-connected.</p></div>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"20 2","pages":"331 - 364"},"PeriodicalIF":0.7,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40062-025-00371-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143925550","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
A conjecture on the composition of localizations on a stratified tensor triangulated category 关于分层张量三角化范畴上局部化组成的猜想
IF 0.7 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2025-04-09 DOI: 10.1007/s40062-025-00367-8
Nicola Bellumat
{"title":"A conjecture on the composition of localizations on a stratified tensor triangulated category","authors":"Nicola Bellumat","doi":"10.1007/s40062-025-00367-8","DOIUrl":"10.1007/s40062-025-00367-8","url":null,"abstract":"<div><p>We study the composition of Bousfield localizations on a tensor triangulated category stratified via the Balmer-Favi support and with noetherian Balmer spectrum. Our aim is to provide reductions via purely axiomatic arguments, allowing us general applications to concrete categories examined in mathematical practice. We propose a conjecture which states that the behaviour of the composition of the localizations depends on the chains of inclusions of the Balmer primes indexing said localizations. We prove this conjecture in the case of finite or low dimensional Balmer spectra.</p></div>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"20 2","pages":"251 - 285"},"PeriodicalIF":0.7,"publicationDate":"2025-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40062-025-00367-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143925518","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 split steinberg modules and steinberg modules 关于拆分斯坦伯格模块和斯坦伯格模块
IF 0.7 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2025-04-09 DOI: 10.1007/s40062-025-00370-z
Daniel Armeanu, Jeremy Miller
{"title":"On split steinberg modules and steinberg modules","authors":"Daniel Armeanu,&nbsp;Jeremy Miller","doi":"10.1007/s40062-025-00370-z","DOIUrl":"10.1007/s40062-025-00370-z","url":null,"abstract":"<div><p>Answering a question of Randal-Williams, we show the natural maps from split Steinberg modules of a Dedekind domain to the associated Steinberg modules are surjective.</p></div>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"20 2","pages":"323 - 329"},"PeriodicalIF":0.7,"publicationDate":"2025-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40062-025-00370-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143925519","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
A localization theorem for cyclic equivariant K-theory 循环等变k理论的一个局部化定理
IF 0.7 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2025-04-04 DOI: 10.1007/s40062-025-00368-7
Jack Carlisle
{"title":"A localization theorem for cyclic equivariant K-theory","authors":"Jack Carlisle","doi":"10.1007/s40062-025-00368-7","DOIUrl":"10.1007/s40062-025-00368-7","url":null,"abstract":"<div><p>For a finite cyclic group <span>(C_n)</span>, we identify Greenlees’ equivariant connective K-theory <span>(kU_{C_n})</span> as an <span>(RO(C_n))</span>-graded localization of the actual connective cover of <span>(KU_{C_n})</span>.</p></div>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"20 2","pages":"287 - 292"},"PeriodicalIF":0.7,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40062-025-00368-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143925541","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
Normed symmetric monoidal categories 赋范对称单一性范畴
IF 0.7 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2025-02-17 DOI: 10.1007/s40062-025-00366-9
Jonathan Rubin
{"title":"Normed symmetric monoidal categories","authors":"Jonathan Rubin","doi":"10.1007/s40062-025-00366-9","DOIUrl":"10.1007/s40062-025-00366-9","url":null,"abstract":"<div><p>We introduce categorical models of <span>(N_infty )</span> spaces, which we call normed symmetric monoidal categories (NSMCs). These are ordinary symmetric monoidal categories equipped with compatible families of norm maps, and when specialized to a particular class of examples, they reveal a connection between the equivariant symmetric monoidal categories of Guillou–May–Merling–Osorno and those of Hill–Hopkins. We also give an operadic interpretation of the Mac Lane coherence theorem and generalize it to include NSMCs. Among other things, this theorem ensures that the classifying space of an NSMC is an <span>(N_infty )</span> space. We conclude by extending our coherence theorem to include NSMCs with strict relations.</p></div>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"20 2","pages":"195 - 250"},"PeriodicalIF":0.7,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143925610","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
Shellability of 3-cut complexes of squared cycle graphs 平方循环图的3切配合物的壳性
IF 0.7 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2025-02-14 DOI: 10.1007/s40062-025-00365-w
Pratiksha Chauhan, Samir Shukla, Kumar Vinayak
{"title":"Shellability of 3-cut complexes of squared cycle graphs","authors":"Pratiksha Chauhan,&nbsp;Samir Shukla,&nbsp;Kumar Vinayak","doi":"10.1007/s40062-025-00365-w","DOIUrl":"10.1007/s40062-025-00365-w","url":null,"abstract":"<div><p>For a positive integer <i>k</i>, the <i>k</i>-cut complex of a graph <i>G</i> is the simplicial complex whose facets are the <span>((|V(G)|-k))</span>-subsets <span>(sigma )</span> of the vertex set <i>V</i>(<i>G</i>) of <i>G</i> such that the induced subgraph of <i>G</i> on <span>(V(G) setminus sigma )</span> is disconnected. These complexes first appeared in the master thesis of Denker and were further studied by Bayer et al. (SIAM J Discrete Math 38(2):1630–1675, 2024). In the same article, Bayer et al. conjectured that for <span>(k ge 3)</span>, the <i>k</i>-cut complexes of squared cycle graphs are shellable. Moreover, they also conjectured about the Betti numbers of these complexes when <span>(k=3)</span>. In this article, we prove these conjectures for <span>(k=3)</span>.</p></div>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"20 1","pages":"163 - 193"},"PeriodicalIF":0.7,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143455437","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
On duoidal (infty )-categories 关于十二指肠(infty ) -分类
IF 0.7 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2025-02-13 DOI: 10.1007/s40062-025-00364-x
Takeshi Torii
{"title":"On duoidal (infty )-categories","authors":"Takeshi Torii","doi":"10.1007/s40062-025-00364-x","DOIUrl":"10.1007/s40062-025-00364-x","url":null,"abstract":"<div><p>A duoidal category is a category equipped with two monoidal structures in which one is (op)lax monoidal with respect to the other. In this paper we introduce duoidal <span>(infty )</span>-categories which are counterparts of duoidal categories in the setting of <span>(infty )</span>-categories. There are three kinds of functors between duoidal <span>(infty )</span>-categories, which are called bilax, double lax, and double oplax monoidal functors. We make three formulations of <span>(infty )</span>-categories of duoidal <span>(infty )</span>-categories according to which functors we take. Furthermore, corresponding to the three kinds of functors, we define bimonoids, double monoids, and double comonoids in duoidal <span>(infty )</span>-categories.</p></div>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"20 1","pages":"125 - 162"},"PeriodicalIF":0.7,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143455434","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
On the homotopy type of partial quotients of certain moment-angle complexes 某些矩角复合体的部分商的同伦型
IF 0.7 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2025-02-13 DOI: 10.1007/s40062-025-00363-y
Xin Fu
{"title":"On the homotopy type of partial quotients of certain moment-angle complexes","authors":"Xin Fu","doi":"10.1007/s40062-025-00363-y","DOIUrl":"10.1007/s40062-025-00363-y","url":null,"abstract":"<div><p>We consider moment-angle complexes associated with skeleta of simplices and determine the homotopy type of their quotient spaces under the diagonal circle action.</p></div>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"20 1","pages":"105 - 123"},"PeriodicalIF":0.7,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143455435","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
Classification of homogeneous functors in manifold calculus 流形微积分中齐次函子的分类
IF 0.7 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2025-02-06 DOI: 10.1007/s40062-025-00362-z
Paul Arnaud Songhafouo Tsopméné, Donald Stanley
{"title":"Classification of homogeneous functors in manifold calculus","authors":"Paul Arnaud Songhafouo Tsopméné,&nbsp;Donald Stanley","doi":"10.1007/s40062-025-00362-z","DOIUrl":"10.1007/s40062-025-00362-z","url":null,"abstract":"<div><p>For any object <i>A</i> in a simplicial model category <span>(mathcal {M})</span>, we construct a topological space <span>(hat{A})</span> which classifies homogeneous functors whose value on <i>k</i> open balls is equivalent to <i>A</i>. This extends a classification result of Weiss for homogeneous functors into topological spaces.</p></div>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"20 1","pages":"63 - 103"},"PeriodicalIF":0.7,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143455540","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
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