The Twisted Homology of Simplicial Set  

作　　者：Meng Meng ZHANG Jing Yan LI Jie WU 

机构地区：[1]School of Mathematical Sciences,Hebei Normal University,Shijiazhuang 050024,P.R.China [2]Yanqi Lake Beijing Institute of Mathematical Sciences and Applications,Beijing 101408,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2022年第10期1781-1802,共22页数学学报（英文版）

基　　金：Supported by NSFC(Grant No.11971144);High-level Scientific Research Foundation of Hebei Province;the start-up research fund from BIMSA;supported by Postgraduate Innovation Funding Project of Hebei Province(Grant No.CXZZBS2022073)。

摘　　要：In this article,we give a generalization of δ-twisted homology introduced by Jingyan Li,Vladimir Vershinin and Jie Wu,called Δ-twisted homology,which enriches the theory of δ-(co)homology introduced by Alexander Grigor’yan,Yuri Muranov and Shing-Tung Yau.We show that the Mayer-Vietoris sequence theorem holds for Δ-twisted homology.Applying the Δ-twisted ideas to Cartesian products,we introduce the notion of Δ-twisted Cartesian product on simplicial sets,which generalizes the classical work of Barratt,Gugenheim and Moore on twisted Cartesian products of simplicial sets.Under certain hypothesis,we show that the coordinate projection of Δ-twisted Cartesian product admits a fibre bundle structure.

关 键 词：Simplicial set Δ-Twisted homology Homotopy type Fibre bundle 

分 类 号：O154.2[理学—数学]