Configuration spaces of an embedding torus and cubical spaces

2006/03/21 by Jean-Philippe Jourdan, Jourdan, Jean-Philippe
Mathematics · #18A30 #20F36 #55R80 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #math.AT #math.GT #msc:18A30 #msc:20F36 #msc:55R80

paper · pdf · doi:10.48550/arxiv.math/0603496

25 pages

arxiv created 2006/03/21 · openalex publication_date 2006/03/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a smooth manifold M obtained as an embedding torus, A U Cx[-1,1], we consider the ordered configuration space F_k(M) of k distinct points in M. We show that there is a homotopical cubical resolution of F_k(M) defined from the configuration spaces of A and C. From it, we deduce a universal method for the computation of the pure braid groups of a manifold. We illustrate the method in the case of the Mobius band.

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