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Journal of Homotopy and Related Structures最新文献

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Hearts and towers in stable (infty )-categories 红心和塔在稳定(infty ) -类别
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2019-05-22 DOI: 10.1007/s40062-019-00237-0
Domenico Fiorenza, Fosco Loregian, Giovanni Luca Marchetti
{"title":"Hearts and towers in stable (infty )-categories","authors":"Domenico Fiorenza,&nbsp;Fosco Loregian,&nbsp;Giovanni Luca Marchetti","doi":"10.1007/s40062-019-00237-0","DOIUrl":"https://doi.org/10.1007/s40062-019-00237-0","url":null,"abstract":"<p>We exploit the equivalence between <i>t</i>-structures and normal torsion theories on a stable <span>(infty )</span>-category to show how a few classical topics in the theory of triangulated categories, i.e., the characterization of bounded <i>t</i>-structures in terms of their hearts, their associated cohomology functors, semiorthogonal decompositions, and the theory of tiltings, as well as the more recent notion of Bridgeland’s slicings, are all particular instances of a single construction, namely, the tower of a morphism associated with a <i>J</i>-slicing of a stable <span>(infty )</span>-category <img>, where <i>J</i> is a totally ordered set equipped with a monotone <span>(mathbb {Z})</span>-action.</p>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"14 4","pages":"993 - 1042"},"PeriodicalIF":0.5,"publicationDate":"2019-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-019-00237-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4875074","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
Involutions on surfaces 曲面上的对合
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2019-05-14 DOI: 10.1007/s40062-019-00236-1
Daniel Dugger
{"title":"Involutions on surfaces","authors":"Daniel Dugger","doi":"10.1007/s40062-019-00236-1","DOIUrl":"https://doi.org/10.1007/s40062-019-00236-1","url":null,"abstract":"<p>We use equivariant surgery to classify all involutions on closed surfaces, up to isomorphism. Work on this problem is classical, dating back to the nineteenth century, with a complete classification finally appearing in the 1990s. In this paper we give a different approach to the classification, using techniques that are more accessible to algebraic topologists as well as a new invariant (which we call the double-Dickson invariant) for distinguishing the “hard” cases.</p>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"14 4","pages":"919 - 992"},"PeriodicalIF":0.5,"publicationDate":"2019-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-019-00236-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4583710","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: 16
Comonad cohomology of track categories 轨道范畴的共上同调
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2019-05-14 DOI: 10.1007/s40062-019-00235-2
David Blanc, Simona Paoli
{"title":"Comonad cohomology of track categories","authors":"David Blanc,&nbsp;Simona Paoli","doi":"10.1007/s40062-019-00235-2","DOIUrl":"https://doi.org/10.1007/s40062-019-00235-2","url":null,"abstract":"<p>We define a comonad cohomology of track categories, and show that it is related via a long exact sequence to the corresponding <span>(({mathcal {S}}!,!mathcal {O}))</span>-cohomology. Under mild hypotheses, the comonad cohomology coincides, up to reindexing, with the <span>(({mathcal {S}}!,!mathcal {O}))</span>-cohomology, yielding an algebraic description of the latter. We also specialize to the case where the track category is a 2-groupoid.</p>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"14 4","pages":"881 - 917"},"PeriodicalIF":0.5,"publicationDate":"2019-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-019-00235-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4585662","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
Matrix factorizations for quantum complete intersections 量子完全交点的矩阵分解
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2019-03-28 DOI: 10.1007/s40062-019-00234-3
Petter Andreas Bergh, Karin Erdmann
{"title":"Matrix factorizations for quantum complete intersections","authors":"Petter Andreas Bergh,&nbsp;Karin Erdmann","doi":"10.1007/s40062-019-00234-3","DOIUrl":"https://doi.org/10.1007/s40062-019-00234-3","url":null,"abstract":"<p>We introduce twisted matrix factorizations for quantum complete intersections of codimension two. For such an algebra, we show that in a given dimension, almost all the indecomposable modules with bounded minimal projective resolutions correspond to such factorizations.</p>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"14 4","pages":"863 - 880"},"PeriodicalIF":0.5,"publicationDate":"2019-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-019-00234-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5089824","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
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
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