Configuration spaces on the sphere and higher loop spaces

Details Configuration spaces on the sphere and higher loop spaces Configuration spaces on the sphere and higher loop spaces

2003-03-24

arxiv.org/abs/math/0303290v1

Mathematics

Algebraic Topology

11 pages

Scientific paper

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.

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