Vers une interprétation galoisienne de la théorie de l'homotopie.

Bertrand Toen (1)

1 LJAD - Laboratoire Jean Alexandre Dieudonné

Given any pointed CW complex (X,x), it is well known that the fondamental group of X pointed at x is naturally isomorphic to the automorphism group of the functor which associates to a locally constant sheaf on X its fibre at x. The purpose of this work is to generalize this fact to higher homotopy. For this we introduce the (infinite) category of locally constant stacks on X, and we prove that the loop-space of endomorphisms of its fibre functor at x is naturally equivalent to the loop space of X based at x.

Domaines: Topologie algébrique [math.AT]; Catégories et ensembles [math.CT]

Bertrand Toen. Vers une interprétation galoisienne de la théorie de l'homotopie.. Cahiers de topologie et géométrie différentielle catégoriques, 2002, 43 (4), pp.257-312. ⟨hal-00773023⟩