A combinatorial model for the path fibration

IF 0.7 4区数学 Q2 MATHEMATICS

Journal of Homotopy and Related Structures Pub Date : 2018-09-29 DOI:10.1007/s40062-018-0216-4

Manuel Rivera, Samson Saneblidze

引用次数: 6

Abstract

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 X we associate a necklical set \({\widehat{{\varvec{\Omega }}}}X\) such that its geometric realization \(|{\widehat{{\varvec{\Omega }}}}X|\), a space built out of gluing cubical cells, is homotopy equivalent to the based loop space on |X| and the differential graded module of chains \(C_*({\widehat{{\varvec{\Omega }}}}X)\) is a differential graded associative algebra generalizing Adams’ cobar construction.

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路径颤振的组合模型

为了描述路径连接简单集几何实现上的路径振动的函数组合模型，我们引入了路径集的抽象概念。特别地，对于任何路径连通的简单集X，我们关联了一个链集\({\widehat{{\varvec{\Omega }}}}X\)，使得它的几何实现\(|{\widehat{{\varvec{\Omega }}}}X|\)(一个由胶合的立方单元构成的空间)同伦等价于X上的基环空间，并且链的微分梯度模\(C_*({\widehat{{\varvec{\Omega }}}}X)\)是推广Adams的cobar构造的微分梯度关联代数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Homotopy and Related Structures MATHEMATICS-

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.