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Journal of Homotopy and Related Structures最新文献

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Derived categories of NDG categories NDG类别的衍生类别
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2021-03-31 DOI: 10.1007/s40062-021-00279-3
Jun-ichi Miyachi, Hiroshi Nagase
{"title":"Derived categories of NDG categories","authors":"Jun-ichi Miyachi,&nbsp;Hiroshi Nagase","doi":"10.1007/s40062-021-00279-3","DOIUrl":"https://doi.org/10.1007/s40062-021-00279-3","url":null,"abstract":"<p>In this paper we study N-differential graded categories and their derived categories. First, we introduce modules over an N-differential graded category. Then we show that they form a Frobenius category and that its homotopy category is triangulated. Second, we study the properties of its derived category and give triangle equivalences of Morita type between derived categories of N-differential graded categories. Finally, we show that this derived category is triangle equivalent to the derived category of some ordinary differential graded category.</p>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"16 2","pages":"191 - 224"},"PeriodicalIF":0.5,"publicationDate":"2021-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-021-00279-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5182032","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 relative K-group in the ETNC, Part II 论etc中的相对k群，第二部分
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2020-11-06 DOI: 10.1007/s40062-020-00267-z
Oliver Braunling
{"title":"On the relative K-group in the ETNC, Part II","authors":"Oliver Braunling","doi":"10.1007/s40062-020-00267-z","DOIUrl":"https://doi.org/10.1007/s40062-020-00267-z","url":null,"abstract":"<p>In a previous paper we showed that, under some assumptions, the relative <i>K</i>-group in the Burns–Flach formulation of the equivariant Tamagawa number conjecture (ETNC) is canonically isomorphic to a <i>K</i>-group of locally compact equivariant modules. Our approach as well as the standard one both involve presentations: One due to Bass–Swan, applied to categories of finitely generated projective modules; and one due to Nenashev, applied to our topological modules without finite generation assumptions. In this paper we provide an explicit isomorphism.</p>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"15 3-4","pages":"597 - 624"},"PeriodicalIF":0.5,"publicationDate":"2020-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-020-00267-z","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4269379","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
Homotopy Gerstenhaber algebras are strongly homotopy commutative 同伦Gerstenhaber代数是强同伦可交换的
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2020-11-01 DOI: 10.1007/s40062-020-00268-y
Matthias Franz
{"title":"Homotopy Gerstenhaber algebras are strongly homotopy commutative","authors":"Matthias Franz","doi":"10.1007/s40062-020-00268-y","DOIUrl":"https://doi.org/10.1007/s40062-020-00268-y","url":null,"abstract":"<p>We show that any homotopy Gerstenhaber algebra is naturally a strongly homotopy commutative (shc) algebra in the sense of Stasheff–Halperin with a homotopy associative structure map. In the presence of certain additional operations corresponding to a <span>(mathbin {cup _1})</span>-product on the bar construction, the structure map becomes homotopy commutative, so that one obtains an shc algebra in the sense of Munkholm.</p>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"15 3-4","pages":"557 - 595"},"PeriodicalIF":0.5,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-020-00268-y","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4051819","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
Homotopic distance between functors 函子间的同伦距离
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2020-10-13 DOI: 10.1007/s40062-020-00269-x
E. Macías-Virgós, D. Mosquera-Lois
{"title":"Homotopic distance between functors","authors":"E. Macías-Virgós,&nbsp;D. Mosquera-Lois","doi":"10.1007/s40062-020-00269-x","DOIUrl":"https://doi.org/10.1007/s40062-020-00269-x","url":null,"abstract":"<p>We introduce a notion of <i>categorical homotopic distance between functors</i> by adapting the notion of homotopic distance in topological spaces, recently defined by the authors, to the context of small categories. Moreover, this notion generalizes the work on categorical LS-category of small categories by Tanaka.</p>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"15 3-4","pages":"537 - 555"},"PeriodicalIF":0.5,"publicationDate":"2020-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-020-00269-x","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4557847","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
Note on Toda brackets 注意Toda括号
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2020-08-28 DOI: 10.1007/s40062-020-00264-2
Samik Basu, David Blanc, Debasis Sen
{"title":"Note on Toda brackets","authors":"Samik Basu,&nbsp;David Blanc,&nbsp;Debasis Sen","doi":"10.1007/s40062-020-00264-2","DOIUrl":"https://doi.org/10.1007/s40062-020-00264-2","url":null,"abstract":"<p>We provide a general definition of Toda brackets in a pointed model category, show how they serve as obstructions to rectification, and explain their relation to the classical stable operations.</p>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"15 3-4","pages":"495 - 510"},"PeriodicalIF":0.5,"publicationDate":"2020-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-020-00264-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5074731","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: 7
Cyclic homology for bornological coarse spaces 竹片粗糙空间的循环同调
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2020-07-24 DOI: 10.1007/s40062-020-00263-3
Luigi Caputi
{"title":"Cyclic homology for bornological coarse spaces","authors":"Luigi Caputi","doi":"10.1007/s40062-020-00263-3","DOIUrl":"https://doi.org/10.1007/s40062-020-00263-3","url":null,"abstract":"<p>The goal of the paper is to define Hochschild and cyclic homology for bornological coarse spaces, i.e., lax symmetric monoidal functors <span>({{,mathrm{mathcal {X}HH},}}_{}^G)</span> and <span>({{,mathrm{mathcal {X}HC},}}_{}^G)</span> from the category <span>(Gmathbf {BornCoarse})</span> of equivariant bornological coarse spaces to the cocomplete stable <span>(infty )</span>-category <span>(mathbf {Ch}_infty )</span> of chain complexes reminiscent of the classical Hochschild and cyclic homology. We investigate relations to coarse algebraic <i>K</i>-theory <span>(mathcal {X}K^G_{})</span> and to coarse ordinary homology?<span>({{,mathrm{mathcal {X}H},}}^G)</span> by constructing a trace-like natural transformation <span>(mathcal {X}K_{}^Grightarrow {{,mathrm{mathcal {X}H},}}^G)</span> that factors through coarse Hochschild (and cyclic) homology. We further compare the forget-control map for <span>({{,mathrm{mathcal {X}HH},}}_{}^G)</span> with the associated generalized assembly map.</p>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"15 3-4","pages":"463 - 493"},"PeriodicalIF":0.5,"publicationDate":"2020-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-020-00263-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4932755","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
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
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