Arrangements of symmetric products of spaces

2003/06/27 by Pavle Blagojevic, Pavle V. M. Blagojević, Vladimir Grujić +6
Mathematics · #52C35 #55S15 #57R19 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT #math.CO #msc:52C35 #msc:55S15 #msc:57R19

paper · pdf · doi:10.48550/arxiv.math/0306399

This is an updated version of the paper. In this version some results (Proposition 1.7., Theorem 1.8, Theorem 1.9, Theorem 1.11) are now reformulated in the greater generality (over integer coefficients). Moreover, we now interpret Theorems 1.8 and 1.11 as a generalization of classical Steenrod's theorem to the case symmetric products of (simple) diagrams of spaces

openalex publication_date 2003/06/27 · arxiv created 2004/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using the topological technique of diagrams of spaces, we calculate the homology of the union and the complement of finite arrangements of subspaces of the form D + SP^n-d(X) in symmetric products SPⁿ(X) where D∈ SP^d(X). As an application we include a computation of the homology of the homotopy end space of the open manifold SPⁿ(M_g,k), where M_g,k is a Riemann surface of genus g punctured at k points, a problem which was originally motivated by the study of commutative (m+k,m)-groups.

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