Journal of Homotopy and Related Structures最新文献_第2页

On the mod 2 cohomology algebra of oriented Grassmannians 论面向格拉斯曼的模 2 同调代数

IF 0.7 4区数学

Journal of Homotopy and Related Structures Pub Date : 2024-06-28 DOI: 10.1007/s40062-024-00350-9

Milica Jovanović, Branislav I. Prvulović

引用次数: 0

Two-sided cartesian fibrations of synthetic ((infty ,1))-categories 合成$$(infty ,1)$$-类的双侧笛卡尔纤度

IF 0.7 4区数学

Journal of Homotopy and Related Structures Pub Date : 2024-06-21 DOI: 10.1007/s40062-024-00348-3

Jonathan Weinberger

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引用次数: 0

Multisimplicial chains and configuration spaces 多简链和构型空间

IF 0.7 4区数学

Journal of Homotopy and Related Structures Pub Date : 2024-05-09 DOI: 10.1007/s40062-024-00344-7

Anibal M. Medina-Mardones, Andrea Pizzi, Paolo Salvatore

引用次数: 0

Homotopy types of diffeomorphism groups of polar Morse–Bott foliations on lens spaces, 2 透镜空间上极性莫尔斯-波特叶形的差分群的同调类型，2

IF 0.7 4区数学

Journal of Homotopy and Related Structures Pub Date : 2024-04-18 DOI: 10.1007/s40062-024-00346-5

Sergiy Maksymenko

引用次数: 0

Diffeological principal bundles and principal infinity bundles 差分主束和主无穷束

IF 0.7 4区数学

Journal of Homotopy and Related Structures Pub Date : 2024-04-15 DOI: 10.1007/s40062-024-00347-4

Emilio Minichiello

引用次数: 0

A Matsumoto type theorem for (GL_n) over rings of non-commutative Laurent polynomials 非交换月桂多项式环上 $$GL_n$$ 的松本类型定理

IF 0.7 4区数学

Journal of Homotopy and Related Structures Pub Date : 2024-04-06 DOI: 10.1007/s40062-024-00345-6

Ryusuke Sugawara

引用次数: 0

A reasonable notion of dimension for singular intersection homology 奇异交点同调的合理维度概念

IF 0.7 4区数学

Journal of Homotopy and Related Structures Pub Date : 2024-04-04 DOI: 10.1007/s40062-024-00343-8

David Chataur, Martintxo Saralegi-Aranguren, Daniel Tanré

{"title":"A reasonable notion of dimension for singular intersection homology","authors":"David Chataur, Martintxo Saralegi-Aranguren, Daniel Tanré","doi":"10.1007/s40062-024-00343-8","DOIUrl":"10.1007/s40062-024-00343-8","url":null,"abstract":"<div>M. Goresky and R. MacPherson intersection homology is also defined from the singular chain complex of a filtered space by H. King, with a key formula to make selections among singular simplexes. This formula needs a notion of dimension for subspaces S of an Euclidean simplex, which is usually taken as the smallest dimension of the skeleta containing S. Later, P. Gajer employed another dimension based on the dimension of polyhedra containing S. This last one allows traces of pullbacks of singular strata in the interior of the domain of a singular simplex. In this work, we prove that the two corresponding intersection homologies are isomorphic for Siebenmann’s CS sets. In terms of King’s paper, this means that polyhedral dimension is a “reasonable” dimension. The proof uses a Mayer-Vietoris argument which needs an adapted subdivision. With the polyhedral dimension, that is a subtle issue. General position arguments are not sufficient and we introduce strong general position. With it, a stability is added to the generic character and we can do an inductive cutting of each singular simplex. This decomposition is realised with pseudo-barycentric subdivisions where the new vertices are not barycentres but close points of them.</div>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140560999","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

Adams operations on the twisted K-theory of compact Lie groups 紧凑李群扭曲 K 理论上的亚当斯运算

IF 0.7 4区数学

Journal of Homotopy and Related Structures Pub Date : 2024-03-18 DOI: 10.1007/s40062-024-00342-9

Chi-Kwong Fok

引用次数: 0

On Vietoris–Rips complexes of finite metric spaces with scale 2 论尺度为 2 的有限度量空间的 Vietoris-Rips 复数

IF 0.7 4区数学

Journal of Homotopy and Related Structures Pub Date : 2024-02-03 DOI: 10.1007/s40062-024-00340-x

Ziqin Feng, Naga Chandra Padmini Nukala

{"title":"On Vietoris–Rips complexes of finite metric spaces with scale 2","authors":"Ziqin Feng, Naga Chandra Padmini Nukala","doi":"10.1007/s40062-024-00340-x","DOIUrl":"10.1007/s40062-024-00340-x","url":null,"abstract":"<div>We examine the homotopy types of Vietoris–Rips complexes on certain finite metric spaces at scale 2. We consider the collections of subsets of ([m]={1, 2, ldots , m}) equipped with symmetric difference metric d, specifically, ({mathcal {F}}^m_n), ({mathcal {F}}_n^mcup {mathcal {F}}^m_{n+1}), ({mathcal {F}}_n^mcup {mathcal {F}}^m_{n+2}), and ({mathcal {F}}_{preceq A}^m). Here ({mathcal {F}}^m_n) is the collection of size n subsets of [m] and ({mathcal {F}}_{preceq A}^m) is the collection of subsets (preceq A) where (preceq ) is a total order on the collections of subsets of [m] and (Asubseteq [m]) (see the definition of (preceq ) in Sect. 1). We prove that the Vietoris–Rips complexes ({{mathcal {V}}}{{mathcal {R}}}({mathcal {F}}^m_n, 2)) and ({{mathcal {V}}}{{mathcal {R}}}({mathcal {F}}_n^mcup {mathcal {F}}^m_{n+1}, 2)) are either contractible or homotopy equivalent to a wedge sum of (S^2)’s; also, the complexes ({{mathcal {V}}}{{mathcal {R}}}({mathcal {F}}_n^mcup {mathcal {F}}^m_{n+2}, 2)) and ({{mathcal {V}}}{{mathcal {R}}}({mathcal {F}}_{preceq A}^m, 2)) are either contractible or homotopy equivalent to a wedge sum of (S^3)’s. We provide inductive formulae for these homotopy types extending the result of Barmak about the independence complexes of Kneser graphs KG(_{2, k}) and the result of Adamaszek and Adams about Vietoris–Rips complexes of hypercube graphs with scale 2.</div>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139677567","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

Associative 2-algebras and nonabelian extensions of associative algebras 关联二元数和关联数的非阿贝尔扩展

IF 0.7 4区数学

Journal of Homotopy and Related Structures Pub Date : 2024-02-01 DOI: 10.1007/s40062-024-00341-w

Yunhe Sheng, You Wang

引用次数: 0