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Article Dans Une Revue Homology, Homotopy and Applications Année : 2005

Higher Monodromy

Résumé

For a given category C and a topological space X, the constant stack on X with stalk C is the stack of locally constant sheaves with values in C. Its global objects are classified by their monodromy, a functor from the Poincare groupoid of X to C. In this paper we recall these notions from the point of view of higher category theory and then define the 2-monodromy of a locally constant stack with values in a 2-category as a 2-functor from the homotopy 2-groupoid into the 2-category. We show that 2-monodromy classifies locally constant stacks on a reasonably well-behaved space X. As an application, we show how to recover from this classification the cohomological version of a classical theorem of Hopf, and we extend it to the non abelian case.

Dates et versions

hal-00133207 , version 1 (23-02-2007)

Identifiants

Citer

Pietro Polesello, Ingo Waschkies. Higher Monodromy. Homology, Homotopy and Applications, 2005, 7, pp.109-150. ⟨hal-00133207⟩
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