Invariance homotopique de certains espaces de configurations

Details Invariance homotopique de certains espaces de configurations Invariance homotopique de certains espaces de configurations

2004-06-30

arxiv.org/abs/math/0407002v1

Mathematics

Algebraic Topology

31 pages, in French

Scientific paper

For a smooth manifold A, we consider the ordered configuration space F_k(AxR) of k distinct points in AxR. We obtain an explicit homotopy construction of the configuration space F_k(AxR) and of the (k-2)-fold suspension of F_k(A). Under certain conditions, we then show that the homotopy types of these two spaces depend only on the homotopy type of A. ----- Pour une variete lisse A, on considere F_k(AxR) l'espace des configurations ordonnees de k particules distinctes dans AxR. On effectue une construction explicite de l'espace de configurations F_k(AxR) et de la suspension (k-2)-ieme de F_k(A). Puis l'on montre que, sous certaines conditions, le type d'homotopie de ces deux espaces ne depend que de celui de A.

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