Higher Monodromy
Abstract
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.
Cite
@article{arxiv.math/0407507,
title = {Higher Monodromy},
author = {Pietro Polesello and Ingo Waschkies},
journal= {arXiv preprint arXiv:math/0407507},
year = {2007}
}
Comments
43 pages. This is a revised version of our preprint RIMS 1432 (11-2003)