2013/08/31 by Martin Palmer
Computer Science · Mathematics · #Advanced Operator Algebra Research #Cohomology #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Manifold (fluid mechanics) #Mathematics #Pure mathematics #Sequence (biology) #Spectral sequence #Topological and Geometric Data Analysis #math.AT #msc:55R80 #msc:57N65
paper · pdf · doi:10.4310/hha.2018.v20.n2.a8
published as Homology, Homotopy and Applications vol. 20 no. 2 (2018) pp. 145-178 · v3: 25 pages
arxiv created 2017/12/19 · openalex publication_date 2018/01/01 · arxiv updated 2018/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Let M be an open, connected manifold. A classical theorem of McDuff and Segal states that the sequence C n (M ) of configuration spaces of n unordered, distinct points in M is homologically stable with coefficients in Z -in each degree, the integral homology is eventually independent of n. The purpose of this paper is to prove that this phenomenon also holds for homology with twisted coefficients. We first define an appropriate notion of finite-degree twisted coefficient system for C n (M ) and then use a spectral sequence argument to deduce the result from the untwisted homological stability result of McDuff and Segal. The result and the methods are generalisations of those of Betley for the symmetric groups.