We show that the homology over a field of the space Lambda(n)Sigma(n)X 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 C(S-n,X) 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 C(S-n,X) coincides with the homology of Lambda(n)Sigma(n)X. In particular we obtain the homology of the unordered configuration spaces on a sphere.

Salvatore, P. (2004). Configuration spaces on the sphere and higher loop spaces. MATHEMATISCHE ZEITSCHRIFT, 248(3), 527-540 [10.1007/s00209-004-0668-6].

Configuration spaces on the sphere and higher loop spaces

SALVATORE, PAOLO
2004-01-01

Abstract

We show that the homology over a field of the space Lambda(n)Sigma(n)X 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 C(S-n,X) 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 C(S-n,X) coincides with the homology of Lambda(n)Sigma(n)X. In particular we obtain the homology of the unordered configuration spaces on a sphere.
2004
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/03 - GEOMETRIA
English
Salvatore, P. (2004). Configuration spaces on the sphere and higher loop spaces. MATHEMATISCHE ZEITSCHRIFT, 248(3), 527-540 [10.1007/s00209-004-0668-6].
Salvatore, P
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/33079
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