2010/10/07 by Sadok Kallel, Walid Taamallah, Kallel, Sadok +1
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #math.AT
paper · pdf · doi:10.48550/arxiv.1010.1507
The earlier version of this paper has now been split into two. Title change. The Euler characteristic computation will appear elsewhere. Many new details worked out in this new version, especially pertaining to section 3 on orbit stratifications and to the proof of main Theorem 1.1. Mistakes and mistatements corrected. 18 pages
openalex publication_date 2010/10/07 · arxiv created 2012/09/14 · arxiv updated 2012/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Permutation products and their various "fat diagonal" subspaces are studied from the topological and geometric point of view. We describe in detail the stabilizer and orbit stratifications related to the permutation action, producing a sharp upper bound for its depth and then paying particular attention to the geometry of the diagonal stratum. We write down an expression for the fundamental group of any permutation product of a connected space X having the homotopy type of a CW complex in terms of π1(X) and H1(X;\bbz). We then prove that the fundamental group of the configuration space of n-points on X, of which multiplicities do not exceed n/2, coincides with H1(X;\bbz). Further results consist in giving conditions for when fat diagonal subspaces of manifolds can be manifolds again. Various examples and homological calculations are included.