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Journal of Homotopy and Related Structures最新文献

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Bianchi’s additional symmetries 比安奇的额外对称性
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2020-07-20 DOI: 10.1007/s40062-020-00262-4
Alexander D. Rahm
{"title":"Bianchi’s additional symmetries","authors":"Alexander D. Rahm","doi":"10.1007/s40062-020-00262-4","DOIUrl":"https://doi.org/10.1007/s40062-020-00262-4","url":null,"abstract":"<p>In a 2012 note in Comptes Rendus Mathématique, the author did try to answer a question of Jean-Pierre Serre; it has recently been announced that the scope of that answer needs an adjustment, and the details of this adjustment are given in the present paper. The original question is the following. Consider the ring of integers?<span>(mathcal {O})</span> in an imaginary quadratic number field, and the Borel–Serre compactification of the quotient of hyperbolic 3–space by <span>(mathrm {SL_2}(mathcal {O}))</span>. Consider the map?<span>(alpha )</span> induced on homology when attaching the boundary into the Borel–Serre compactification. <i>How can one determine the kernel of</i>?<span>(alpha )</span> <i>(in degree 1) ?</i> Serre used a global topological argument and obtained the rank of the kernel of?<span>(alpha )</span>. He added the question what submodule precisely this kernel is.</p>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"15 3-4","pages":"455 - 462"},"PeriodicalIF":0.5,"publicationDate":"2020-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-020-00262-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4792757","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
Descent theory and mapping spaces 下降理论和映射空间
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2020-07-03 DOI: 10.1007/s40062-020-00261-5
Nicholas J. Meadows
{"title":"Descent theory and mapping spaces","authors":"Nicholas J. Meadows","doi":"10.1007/s40062-020-00261-5","DOIUrl":"https://doi.org/10.1007/s40062-020-00261-5","url":null,"abstract":"<p>The purpose of this paper is to develop a theory of <span>((infty , 1))</span>-stacks, in the sense of Hirschowitz–Simpson’s ‘Descent Pour Les n–Champs’, using the language of quasi-category theory and the author’s local Joyal model structure. The main result is a characterization of <span>((infty , 1))</span>-stacks in terms of mapping space presheaves. An important special case of this theorem gives a sufficient condition for the presheaf of quasi-categories associated to a presheaf of model categories to be a higher stack. In the final section, we apply this result to construct the higher stack of unbounded complexes associated to a ringed site.</p>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"15 3-4","pages":"417 - 453"},"PeriodicalIF":0.5,"publicationDate":"2020-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-020-00261-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4125863","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: 2
Higher equivariant and invariant topological complexities 更高的等变和不变拓扑复杂性
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2020-06-21 DOI: 10.1007/s40062-020-00260-6
Marzieh Bayeh, Soumen Sarkar
{"title":"Higher equivariant and invariant topological complexities","authors":"Marzieh Bayeh,&nbsp;Soumen Sarkar","doi":"10.1007/s40062-020-00260-6","DOIUrl":"https://doi.org/10.1007/s40062-020-00260-6","url":null,"abstract":"<p>In this paper we introduce concepts of higher equivariant and invariant topological complexities and study their properties. Then we compare them with equivariant LS-category. We give lower and upper bounds for these new invariants. We compute some of these invariants for moment angle complexes.</p>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"15 3-4","pages":"397 - 416"},"PeriodicalIF":0.5,"publicationDate":"2020-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-020-00260-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4682495","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: 8
Verifying the Hilali conjecture up to formal dimension twenty 验证Hilali猜想直到形式维数20
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2020-03-12 DOI: 10.1007/s40062-020-00256-2
Spencer Cattalani, Aleksandar Milivojević
{"title":"Verifying the Hilali conjecture up to formal dimension twenty","authors":"Spencer Cattalani,&nbsp;Aleksandar Milivojević","doi":"10.1007/s40062-020-00256-2","DOIUrl":"https://doi.org/10.1007/s40062-020-00256-2","url":null,"abstract":"<p>We prove that in formal dimension <span>(le 20)</span> the Hilali conjecture holds, i.e. that the total dimension of the rational homology bounds from above the total dimension of the rational homotopy for a simply connected rationally elliptic space.</p>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"15 2","pages":"323 - 331"},"PeriodicalIF":0.5,"publicationDate":"2020-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-020-00256-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4803190","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: 4
Twisting structures and morphisms up to strong homotopy 到强同伦的扭曲结构和态射
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2019-11-08 DOI: 10.1007/s40062-019-00249-w
Kathryn Hess, Paul-Eugène Parent, Jonathan Scott
{"title":"Twisting structures and morphisms up to strong homotopy","authors":"Kathryn Hess,&nbsp;Paul-Eugène Parent,&nbsp;Jonathan Scott","doi":"10.1007/s40062-019-00249-w","DOIUrl":"https://doi.org/10.1007/s40062-019-00249-w","url":null,"abstract":"<p>We define twisted composition products of symmetric sequences via classifying morphisms rather than twisting cochains. Our approach allows us to establish an adjunction that simultaneously generalizes a classic one for algebras and coalgebras, and the bar-cobar adjunction for quadratic operads. The comonad associated to this adjunction turns out to be, in several cases, a standard Koszul construction. The associated Kleisli categories are the “strong homotopy” morphism categories. In an appendix, we study the co-ring associated to the canonical morphism of cooperads <img>, which is exactly the two-sided Koszul resolution of the associative operad <img>, also known as the Alexander-Whitney co-ring.</p>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"15 1","pages":"185 - 222"},"PeriodicalIF":0.5,"publicationDate":"2019-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-019-00249-w","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4353225","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
Correction to: Wrong way maps in uniformly finite homology and homology of groups 修正:一致有限同调和群同调中的错误映射
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2019-09-21 DOI: 10.1007/s40062-019-00246-z
Alexander Engel
{"title":"Correction to: Wrong way maps in uniformly finite homology and homology of groups","authors":"Alexander Engel","doi":"10.1007/s40062-019-00246-z","DOIUrl":"https://doi.org/10.1007/s40062-019-00246-z","url":null,"abstract":"","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"14 4","pages":"1143 - 1144"},"PeriodicalIF":0.5,"publicationDate":"2019-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-019-00246-z","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5142177","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
A model structure via orbit spaces for equivariant homotopy 等变同伦的轨道空间模型结构
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2019-06-26 DOI: 10.1007/s40062-019-00241-4
Mehmet Akif Erdal, Aslı Güçlükan İlhan
{"title":"A model structure via orbit spaces for equivariant homotopy","authors":"Mehmet Akif Erdal,&nbsp;Aslı Güçlükan İlhan","doi":"10.1007/s40062-019-00241-4","DOIUrl":"https://doi.org/10.1007/s40062-019-00241-4","url":null,"abstract":"<p>Let <i>G</i> be discrete group and <span>(mathcal F)</span> be a collection of subgroups of <i>G</i>. We show that there exists a left induced model structure on the category of right <i>G</i>-simplicial sets, in which the weak equivalences and cofibrations are the maps that induce weak equivalences and cofibrations on <i>H</i>-orbits for all <i>H</i> in <span>(mathcal F)</span>. This gives a model categorical criterion for maps that induce weak equivalences on <i>H</i>-orbits to be weak equivalences in the <span>(mathcal F)</span>-model structure.</p>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"14 4","pages":"1131 - 1141"},"PeriodicalIF":0.5,"publicationDate":"2019-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-019-00241-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5007558","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: 6
Cohomology of infinite groups realizing fusion systems 实现融合系统的无穷群的上同调
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2019-06-07 DOI: 10.1007/s40062-019-00240-5
Muhammed Said Gündoğan, Ergün Yalçın
{"title":"Cohomology of infinite groups realizing fusion systems","authors":"Muhammed Said Gündoğan,&nbsp;Ergün Yalçın","doi":"10.1007/s40062-019-00240-5","DOIUrl":"https://doi.org/10.1007/s40062-019-00240-5","url":null,"abstract":"<p>Given a fusion system <span>({mathcal {F}})</span> defined on a <i>p</i>-group <i>S</i>, there exist infinite group models, constructed by Leary and Stancu, and Robinson, that realize <span>({mathcal {F}})</span>. We study these models when <span>({mathcal {F}})</span> is a fusion system of a finite group <i>G</i> and prove a theorem which relates the cohomology of an infinite group model <span>(pi )</span> to the cohomology of the group <i>G</i>. We show that for the groups <i>GL</i>(<i>n</i>,?2), where <span>(nge 5)</span>, the cohomology of the infinite group obtained using the Robinson model is different than the cohomology of the fusion system. We also discuss the signalizer functors <span>(Prightarrow Theta (P))</span> for infinite group models and obtain a long exact sequence for calculating the cohomology of a centric linking system with twisted coefficients.</p>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"14 4","pages":"1103 - 1130"},"PeriodicalIF":0.5,"publicationDate":"2019-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-019-00240-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4305775","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: 1
Dense products in fundamental groupoids 基本群类群中的致密积
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2019-06-03 DOI: 10.1007/s40062-019-00238-z
Jeremy Brazas
{"title":"Dense products in fundamental groupoids","authors":"Jeremy Brazas","doi":"10.1007/s40062-019-00238-z","DOIUrl":"https://doi.org/10.1007/s40062-019-00238-z","url":null,"abstract":"<p>Infinitary operations, such as products indexed by countably infinite linear orders, arise naturally in the context of fundamental groups and groupoids. Despite the fact that the usual binary operation of the fundamental group determines the operation of the fundamental groupoid, we show that, for a locally path-connected metric space, the well-definedness of countable dense products in the fundamental group need not imply the well-definedness of countable dense products in the fundamental groupoid. Additionally, we show the fundamental groupoid <span>(Pi _1(X))</span> has well-defined dense products if and only if <i>X</i> admits a generalized universal covering space.</p>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"14 4","pages":"1083 - 1102"},"PeriodicalIF":0.5,"publicationDate":"2019-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-019-00238-z","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4127323","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: 2
Minimality in diagrams of simplicial sets 简单集图的极小性
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2019-05-30 DOI: 10.1007/s40062-019-00239-y
Carles Broto, Ramón Flores, Carlos Giraldo
{"title":"Minimality in diagrams of simplicial sets","authors":"Carles Broto,&nbsp;Ramón Flores,&nbsp;Carlos Giraldo","doi":"10.1007/s40062-019-00239-y","DOIUrl":"https://doi.org/10.1007/s40062-019-00239-y","url":null,"abstract":"<p>We formulate the concept of minimal fibration in the context of fibrations in the model category <span>({mathbf {S}}^{mathcal {C}})</span> of <span>({mathcal {C}})</span>-diagrams of simplicial sets, for a small index category <span>({mathcal {C}})</span>. When <span>({mathcal {C}})</span> is an <i>EI</i>-category satisfying some mild finiteness restrictions, we show that every fibration of <span>({mathcal {C}})</span>-diagrams admits a well-behaved minimal model. As a consequence, we establish a classification theorem for fibrations in <span>({mathbf {S}}^{mathcal {C}})</span> over a constant diagram, generalizing the classification theorem of Barratt, Gugenheim, and Moore for simplicial fibrations (Barratt?et?al. in Am J Math 81:639–657, 1959).</p>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"14 4","pages":"1043 - 1082"},"PeriodicalIF":0.5,"publicationDate":"2019-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-019-00239-y","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5160383","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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