The twisted homology of simplicial set
type: Item
instance of: scholarly article
title: The twisted homology of simplicial set
author: Jingyan Li
author: Jie Wu
author: Mengmeng Zhang
publication date: 2022-11-11T00:00:00Z
review text: The paper gives the \(\Delta\)-twisted homology as a generalization of the \(\delta\)-twisted homology introduced by Jingyan Li, Vladimir Vershinin and Jie Wu [\textit{J. Y. Li} et al., Homology Homotopy Appl. 19, No. 2, 111--130 (2017; Zbl 1384.55016)]. This enriches the theory of \(\delta\)-(co)homology introduced by Alexander Grigoryan, Yuri Muranov, and Shing-Tung Yau [\textit{A. Grigor'yan} et al., J. Homotopy Relat. Struct. 11, No. 2, 209--230 (2016; Zbl 1353.05056)]. The paper proves that the Mayer-Vietoris sequence holds for \(\Delta\)-twisted homology, and the paper introduces the notion of \(\Delta\)-twisted Cartesian product on simplicial sets, which generalizes the classical work of Barratt, Gugenheim and Moore on twisted Cartesian products of simplicial sets [\textit{M. Barratt} et al., Am. J. Math. 81, 639--657 (1959; Zbl 0127.39002)]. Under certain hypotheses, the paper shows that the coordinate projection of \(\Delta\)-twisted Cartesian products admits a fibre bundle structure.
reviewed by: Shiquan Ren
Mathematics Subject Classification ID: 55U10
Mathematics Subject Classification ID: 55P35
Mathematics Subject Classification ID: 55R35
zbMATH DE Number: 7615089
zbMATH Keywords: simplicial set
zbMATH Keywords: \(\Delta\)-twisted homology
zbMATH Keywords: homotopy type
zbMATH Keywords: fibre bundle
MaRDI profile type: Publication
full work available at URL: s10114-022-2190-3
OpenAlex ID: W4308470498
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DOI: 10.1007/S10114-022-2190-3
published in: Acta Mathematica Sinica, English Series
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description: scientific article; zbMATH DE number 7615089