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Article Dans Une Revue Cahiers de topologie et géométrie différentielle catégoriques Année : 2002

Toward a Galoisian interpretation of homotopy theory

B. Toen

Résumé

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.

Dates et versions

hal-00022950 , version 1 (16-04-2006)

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Citer

B. Toen. Toward a Galoisian interpretation of homotopy theory. Cahiers de topologie et géométrie différentielle catégoriques, 2002, 43, pp.257-312. ⟨hal-00022950⟩
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