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Journal of Homotopy and Related Structures最新文献

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Some characterizations of acyclic maps 无环映射的一些特征
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2019-03-04 DOI: 10.1007/s40062-019-00231-6
George Raptis
{"title":"Some characterizations of acyclic maps","authors":"George Raptis","doi":"10.1007/s40062-019-00231-6","DOIUrl":"https://doi.org/10.1007/s40062-019-00231-6","url":null,"abstract":"<p>We discuss two categorical characterizations of the class of acyclic maps between spaces. The first one is in terms of the higher categorical notion of an epimorphism. The second one employs the notion of a balanced map, that is, a map whose homotopy pullbacks along <span>(pi _0)</span>-surjective maps define also homotopy pushouts. We also identify the modality in the homotopy theory of spaces that is defined by the class of acyclic maps, and discuss the content of the generalized Blakers–Massey theorem for this modality.</p>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"14 3","pages":"773 - 785"},"PeriodicalIF":0.5,"publicationDate":"2019-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-019-00231-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4174404","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: 13
Tate cohomology of connected k-theory for elementary abelian groups revisited 初等阿贝尔群的连通k理论的Tate上同调
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2019-01-10 DOI: 10.1007/s40062-018-00229-6
Po Hu, Igor Kriz, Petr Somberg
{"title":"Tate cohomology of connected k-theory for elementary abelian groups revisited","authors":"Po Hu,&nbsp;Igor Kriz,&nbsp;Petr Somberg","doi":"10.1007/s40062-018-00229-6","DOIUrl":"https://doi.org/10.1007/s40062-018-00229-6","url":null,"abstract":"<p>Tate cohomology (as well as Borel homology and cohomology) of connective K-theory for <span>(G=({mathbb {Z}}/2)^n)</span> was completely calculated by Bruner and Greenlees (The connective K-theory of finite groups, 2003). In this note, we essentially redo the calculation by a different, more elementary method, and we extend it to <span>(p&gt;2)</span> prime. We also identify the resulting spectra, which are products of Eilenberg–Mac Lane spectra, and finitely many finite Postnikov towers. For <span>(p=2)</span>, we also reconcile our answer completely with the result of [2], which is in a different form, and hence the comparison involves some non-trivial combinatorics.</p>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"14 3","pages":"749 - 772"},"PeriodicalIF":0.5,"publicationDate":"2019-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-018-00229-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4420179","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 multiplicative K-theoretic model of Voevodsky’s motivic K-theory spectrum Voevodsky的动机k理论谱的乘法k理论模型
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2018-11-28 DOI: 10.1007/s40062-018-0227-1
Youngsoo Kim
{"title":"A multiplicative K-theoretic model of Voevodsky’s motivic K-theory spectrum","authors":"Youngsoo Kim","doi":"10.1007/s40062-018-0227-1","DOIUrl":"https://doi.org/10.1007/s40062-018-0227-1","url":null,"abstract":"<p>Voevodsky defined a motivic spectrum representing algebraic <i>K</i>-theory, and Panin, Pimenov, and R?ndigs described its ring structure up to homotopy. We construct a motivic symmetric spectrum with a strict ring structure. Then we show that these spectra are stably equivalent and that their ring structures are compatible up to homotopy.</p>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"14 3","pages":"663 - 690"},"PeriodicalIF":0.5,"publicationDate":"2018-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-018-0227-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5035266","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
Equivariant chromatic localizations and commutativity 等变色局域化与交换性
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2018-11-27 DOI: 10.1007/s40062-018-0226-2
Michael A. Hill
{"title":"Equivariant chromatic localizations and commutativity","authors":"Michael A. Hill","doi":"10.1007/s40062-018-0226-2","DOIUrl":"https://doi.org/10.1007/s40062-018-0226-2","url":null,"abstract":"<p>In this paper, we study the extent to which Bousfield and finite localizations relative to a thick subcategory of equivariant finite spectra preserve various kinds of highly structured multiplications. Along the way, we describe some basic, useful results for analyzing categories of acyclics in equivariant spectra, and we show that Bousfield localization with respect to an ordinary spectrum (viewed as an equivariant spectrum with trivial action) always preserves equivariant commutative ring spectra.</p>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"14 3","pages":"647 - 662"},"PeriodicalIF":0.5,"publicationDate":"2018-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-018-0226-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5500518","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: 9
Yoga of commutators in DSER elementary orthogonal group DSER初等正交群中换向子的瑜伽
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2018-11-15 DOI: 10.1007/s40062-018-0223-5
A. A. Ambily
{"title":"Yoga of commutators in DSER elementary orthogonal group","authors":"A. A. Ambily","doi":"10.1007/s40062-018-0223-5","DOIUrl":"https://doi.org/10.1007/s40062-018-0223-5","url":null,"abstract":"<p>In this article, we consider the Dickson-Siegel-Eichler-Roy (DSER) elementary orthogonal subgroup of the orthogonal group of a non-degenerate quadratic space with a hyperbolic summand over a commutative ring, introduced by Roy. We prove a set of commutator relations among the elementary generators of the DSER elementary orthogonal group. As an application, we prove that this group is perfect and an action version of the Quillen’s local-global principle for this group is proved. This affirmatively answers a question of Rao in his Ph.D. thesis.</p>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"14 2","pages":"595 - 610"},"PeriodicalIF":0.5,"publicationDate":"2018-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-018-0223-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4626374","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
Stabilization of derivators revisited 再论衍生品的稳定性
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2018-11-10 DOI: 10.1007/s40062-018-0224-4
Ian Coley
{"title":"Stabilization of derivators revisited","authors":"Ian Coley","doi":"10.1007/s40062-018-0224-4","DOIUrl":"https://doi.org/10.1007/s40062-018-0224-4","url":null,"abstract":"<p>We revisit and improve Alex Heller’s results on the stabilization of derivators in Heller (J Pure Appl Algebra 115(2):113–130, 1997), recovering his results entirely. Along the way we give some details of the localization theory of derivators and prove some new results in that vein.</p>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"14 2","pages":"525 - 577"},"PeriodicalIF":0.5,"publicationDate":"2018-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-018-0224-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4432116","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: 5
The Dold–Thom theorem via factorization homology 因式分解同调的Dold-Thom定理
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2018-11-10 DOI: 10.1007/s40062-018-0219-1
Lauren Bandklayder
{"title":"The Dold–Thom theorem via factorization homology","authors":"Lauren Bandklayder","doi":"10.1007/s40062-018-0219-1","DOIUrl":"https://doi.org/10.1007/s40062-018-0219-1","url":null,"abstract":"<p>We give a new proof of the classical Dold–Thom theorem using factorization homology. Our method is direct and conceptual, avoiding the Eilenberg–Steenrod axioms entirely in favor of a more general geometric argument.</p>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"14 2","pages":"579 - 593"},"PeriodicalIF":0.5,"publicationDate":"2018-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-018-0219-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4430487","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
The Koszul–Tate type resolution for Gerstenhaber–Batalin–Vilkovisky algebras Gerstenhaber-Batalin-Vilkovisky代数的Koszul-Tate型解析
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2018-10-25 DOI: 10.1007/s40062-018-0218-2
Jeehoon Park, Donggeon Yhee
{"title":"The Koszul–Tate type resolution for Gerstenhaber–Batalin–Vilkovisky algebras","authors":"Jeehoon Park,&nbsp;Donggeon Yhee","doi":"10.1007/s40062-018-0218-2","DOIUrl":"https://doi.org/10.1007/s40062-018-0218-2","url":null,"abstract":"<p>Tate provided an <i>explicit</i> way to kill a nontrivial homology class of a commutative differential graded algebra over a commutative noetherian ring <i>R</i> in Tate (Ill J Math 1:14–27, 1957). The goal of this article is to generalize his result to the case of GBV (Gerstenhaber–Batalin–Vilkovisky) algebras and, more generally, the descendant <span>(L_infty )</span>-algebras. More precisely, for a given GBV algebra <span>((mathcal {A}=oplus _{mge 0}mathcal {A}_m, delta , ell _2^delta ))</span>, we provide another <i>explicit</i> GBV algebra <span>((widetilde{mathcal {A}}=oplus _{mge 0}widetilde{mathcal {A}}_m, widetilde{delta }, ell _2^{widetilde{delta }}))</span> such that its total homology is the same as the degree zero part of the homology <span>(H_0(mathcal {A}, delta ))</span> of the given GBV algebra <span>((mathcal {A}, delta , ell _2^delta ))</span>.</p>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"14 2","pages":"455 - 475"},"PeriodicalIF":0.5,"publicationDate":"2018-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-018-0218-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4985810","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 combinatorial model for the path fibration 路径颤振的组合模型
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2018-09-29 DOI: 10.1007/s40062-018-0216-4
Manuel Rivera, Samson Saneblidze
{"title":"A combinatorial model for the path fibration","authors":"Manuel Rivera,&nbsp;Samson Saneblidze","doi":"10.1007/s40062-018-0216-4","DOIUrl":"https://doi.org/10.1007/s40062-018-0216-4","url":null,"abstract":"<p>We introduce the abstract notion of a necklical set in order to describe a functorial combinatorial model of the path fibration over the geometric realization of a path connected simplicial set. In particular, to any path connected simplicial set <i>X</i> we associate a necklical set <span>({widehat{{varvec{Omega }}}}X)</span> such that its geometric realization <span>(|{widehat{{varvec{Omega }}}}X|)</span>, a space built out of gluing cubical cells, is homotopy equivalent to the based loop space on |<i>X</i>| and the differential graded module of chains <span>(C_*({widehat{{varvec{Omega }}}}X))</span> is a differential graded associative algebra generalizing Adams’ cobar construction.</p>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"14 2","pages":"393 - 410"},"PeriodicalIF":0.5,"publicationDate":"2018-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-018-0216-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5133041","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
Topology of scrambled simplices 乱序单形的拓扑结构
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2018-09-27 DOI: 10.1007/s40062-018-0214-6
Dmitry N. Kozlov
{"title":"Topology of scrambled simplices","authors":"Dmitry N. Kozlov","doi":"10.1007/s40062-018-0214-6","DOIUrl":"https://doi.org/10.1007/s40062-018-0214-6","url":null,"abstract":"<p>In this paper we define a?family of topological spaces, which contains and vastly generalizes the higher-dimensional Dunce hats. Our definition is purely combinatorial, and is phrased in terms of identifications of boundary simplices of a?standard <i>d</i>-simplex. By virtue of the construction, the obtained spaces may be indexed by words, and they automatically carry the structure of a?<span>(Delta )</span>-complex. As our main result, we completely determine the homotopy type of these spaces. In fact, somewhat surprisingly, we are able to prove that each of them is either contractible or homotopy equivalent to an?odd-dimensional sphere. We develop the language to determine the homotopy type directly from the combinatorics of the indexing word. As added benefit of our investigation, we are able to emulate the Dunce hat phenomenon, and to obtain a?large family of both <span>(Delta )</span>-complexes, as well as simplicial complexes, which are contractible, but not collapsible.</p>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"14 2","pages":"371 - 391"},"PeriodicalIF":0.5,"publicationDate":"2018-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-018-0214-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5064663","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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