Multisimplicial chains and configuration spaces

IF 0.7 4区数学 Q2 MATHEMATICS

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

Abstract

We define an \(E_\infty \)-coalgebra structure on the chains of multisimplicial sets. Our primary focus is on the surjection chain complexes of McClure-Smith, for which we construct a zig-zag of complexity preserving quasi-isomorphisms of \(E_\infty \)-coalgebras relating them to both the singular chains on configuration spaces and the Barratt–Eccles chain complexes.

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多简链和构型空间

我们在多简集链上定义了一个 \(E_\infty \)-代数结构。我们的主要关注点是麦克卢尔-史密斯（McClure-Smith）的投射链复数，为此我们构建了一个复杂性保存的 \(E_\infty \)-coalgebras 准同构的 "之 "字形结构，将它们与配置空间上的奇异链和巴拉特-埃克尔斯链复数联系起来。

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.