Title: Configuration spaces on the sphere and higher loop spaces
Author: Paolo Salvatore
AMS classification numbers: 55P48, 55R80, 55S12
xxx number: math.AT/0303290
Address: Dipartimento di Matematica,
Universita` di Roma "Tor Vergata",
Via della Ricerca Scientifica 1,
00133 Roma, Italy
e-mail: salvator@mat.uniroma2.it
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 depend 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.