2014/09/10 by Jeremy Miller, J. J. Miller, Martin Palmer
Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Algebraic structures and combinatorial models #Combinatorics #Computer science #Fibration #Homology (biology) #Homotopy #Homotopy and Cohomology in Algebraic Topology #Library science #Mathematics #Miller #Pure mathematics #math.AT #msc:55R35 #msc:55R65 #msc:57T30
paper · pdf · doi:10.1093/qmath/hau030
published as Q. J. Math. vol. 66 no. 1 (2015) pp. 265-284 · 21 pages. This note supersedes Section 2 of arXiv:1306.6896v1, which has been split in half for length reasons
arxiv created 2014/09/10 · openalex publication_date 2014/12/01 · arxiv updated 2018/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The purpose of this note is to clarify some details in McDuff and Segal's proof of the group-completion theorem in McDuff and Segal [Homology fibrations and the ‘group-completion’ theorem, Invent. Math.31 (1975/76), 279–284] and generalize this and the homology fibration criterion of McDuff [Configuration spaces of positive and negative particles, Topology14 (1975), 91–107] to homology with twisted coefficients. This will be used in Miller and Palmer [Scanning for oriented configuration spaces, preprint, 2014] to identify the limiting homology of ‘oriented’ configuration spaces, which doubly cover the classical configuration spaces of distinct unordered points in a manifold.