Configuration spaces on the sphere and higher loop spaces

2003/03/24 by Paolo Salvatore, Salvatore, Paolo
Mathematics · #55P48 #55R80 #55S12 #Algebraic Topology (math.AT) #FOS: Mathematics #math.AT #msc:55P48 #msc:55R80 #msc:55S12

paper · pdf · doi:10.48550/arxiv.math/0303290

11 pages

arxiv created 2003/03/24 · arxiv updated 2009/11/30

Abstract

We show that the homology over a field of the space of free maps from the n-sphere to the n-fold suspension of X depends only on the cohomology algebra of X and compute it explicitly. We compute also the homology of the closely related labelled configuration space on the n-sphere with labels in X and of its completion, that depends only on the homology of X. In many but not all cases the homology of the configuration space coincides with the homology of the mapping space. In particular we obtain the homology of the unordered configuration spaces on a sphere.

Related

• Configuration spaces in algebraic topology
• Homology of spaces of regular loops in the sphere
• Lie algebras and the (co)homology of configuration spaces
• Stability in the homology of configuration spaces of high dimensional manifolds
• On the Homology of Configuration Spaces C((M,M_o)× \bold Rⁿ; X)