Journal of Homotopy and Related Structures最新文献

Periodic self maps and thick ideals in the stable motivic homotopy category over ({mathbb {C}}) at odd primes ({mathbb {C}})上奇素数下稳定动机同伦范畴的周期自映射与厚理想

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2023-11-23 DOI: 10.1007/s40062-023-00337-y

Sven-Torben Stahn

引用次数: 0

The homotopy of the (KU_G)-local equivariant sphere spectrum (KU_G) -局部等变球谱的同伦

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2023-11-20 DOI: 10.1007/s40062-023-00336-z

Tanner N. Carawan, Rebecca Field, Bertrand J. Guillou, David Mehrle, Nathaniel J. Stapleton

引用次数: 0

Prismatic cohomology and p-adic homotopy theory 棱镜上同调与p进同伦理论

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2023-11-13 DOI: 10.1007/s40062-023-00335-0

Tobias Shin

引用次数: 0

Weak cartesian properties of simplicial sets 简单集的弱笛卡儿性质

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2023-11-10 DOI: 10.1007/s40062-023-00334-1

Carmen Constantin, Tobias Fritz, Paolo Perrone, Brandon T. Shapiro

{"title":"Weak cartesian properties of simplicial sets","authors":"Carmen Constantin, Tobias Fritz, Paolo Perrone, Brandon T. Shapiro","doi":"10.1007/s40062-023-00334-1","DOIUrl":"10.1007/s40062-023-00334-1","url":null,"abstract":"<div>Many special classes of simplicial sets, such as the nerves of categories or groupoids, the 2-Segal sets of Dyckerhoff and Kapranov, and the (discrete) decomposition spaces of Gálvez, Kock, and Tonks, are characterized by the property of sending certain commuting squares in the simplex category (Delta ) to pullback squares of sets. We introduce weaker analogues of these properties called completeness conditions, which require squares in (Delta ) to be sent to weak pullbacks of sets, defined similarly to pullback squares but without the uniqueness property of induced maps. We show that some of these completeness conditions provide a simplicial set with lifts against certain subsets of simplices first introduced in the theory of database design. We also provide reduced criteria for checking these properties using factorization results for pushouts squares in (Delta ), which we characterize completely, along with several other classes of squares in (Delta ). Examples of simplicial sets with completeness conditions include quasicategories, many of the compositories and gleaves of Flori and Fritz, and bar constructions for algebras of certain classes of monads. The latter is our motivating example.</div>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135087722","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

On the K-theory of (mathbb {Z})-categories 论(mathbb {Z}) -范畴的k理论

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2023-11-04 DOI: 10.1007/s40062-023-00333-2

Eugenia Ellis, Rafael Parra

引用次数: 0

Self-closeness numbers of rational mapping spaces 有理映射空间的自闭数

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2023-10-11 DOI: 10.1007/s40062-023-00332-3

Yichen Tong

{"title":"Self-closeness numbers of rational mapping spaces","authors":"Yichen Tong","doi":"10.1007/s40062-023-00332-3","DOIUrl":"10.1007/s40062-023-00332-3","url":null,"abstract":"<div>For a closed connected oriented manifold M of dimension 2n, it was proved by Møller and Raussen that the components of the mapping space from M to (S^{2n}) have exactly two different rational homotopy types. However, since this result was proved by the algebraic models for the components, it is unclear whether other homotopy invariants distinguish their rational homotopy types or not. The self-closeness number of a connected CW complex is the least integer k such that any of its self-maps inducing an isomorphism in (pi _*) for (*le k) is a homotopy equivalence, and there is no result on the components of mapping spaces so far. For a rational Poincaré complex X of dimension 2n with finite (pi _1), we completely determine the self-closeness numbers of the rationalized components of the mapping space from X to (S^{2n}) by using their Brown–Szczarba models. As a corollary, we show that the self-closeness number does distinguish the rational homotopy types of the components. Since a closed connected oriented manifold is a rational Poincaré complex, our result partially generalizes that of Møller and Raussen.</div>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136208974","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

Comparison of the colimit and the 2-colimit 极限与2极限的比较

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2023-10-04 DOI: 10.1007/s40062-023-00331-4

Ilia Pirashvili

引用次数: 0

Localization (C^*-)algebras and index pairing 定位(C^*-)代数和索引配对

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2022-11-24 DOI: 10.1007/s40062-022-00320-z

Hang Wang, Chaohua Zhang, Dapeng Zhou

引用次数: 0

The (mathbb {R})-local homotopy theory of smooth spaces 光滑空间的(mathbb {R}) -局部同伦理论

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2022-11-11 DOI: 10.1007/s40062-022-00318-7

Severin Bunk

{"title":"The (mathbb {R})-local homotopy theory of smooth spaces","authors":"Severin Bunk","doi":"10.1007/s40062-022-00318-7","DOIUrl":"10.1007/s40062-022-00318-7","url":null,"abstract":"<div>Simplicial presheaves on cartesian spaces provide a general notion of smooth spaces. There is a corresponding smooth version of the singular complex functor, which maps smooth spaces to simplicial sets. We consider the localisation of the (projective or injective) model category of smooth spaces at the morphisms which become weak equivalences under the singular complex functor. We prove that this localisation agrees with a motivic-style (mathbb {R})-localisation of the model category of smooth spaces. Further, we exhibit the singular complex functor for smooth spaces as one of several Quillen equivalences between model categories for spaces and the above (mathbb {R})-local model category of smooth spaces. In the process, we show that the singular complex functor agrees with the homotopy colimit functor up to a natural zig-zag of weak equivalences. We provide a functorial fibrant replacement in the (mathbb {R})-local model category of smooth spaces and use this to compute mapping spaces in terms of singular complexes. Finally, we explain the relation of our fibrant replacement to the concordance sheaf construction introduced recently by Berwick-Evans, Boavida de Brito and Pavlov.\u0000</div>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40062-022-00318-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4477160","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: 4

Multifunctorial K-theory is an equivalence of homotopy theories 多泛函k理论是同伦理论的等价

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2022-11-01 DOI: 10.1007/s40062-022-00317-8

Niles Johnson, Donald Yau

引用次数: 0