EMIS/ELibM Electronic Journals

Outdated Archival Version

These pages are not updated anymore. They reflect the state of 22 June 2005. For the current production of this journal, please refer to http://intlpress.com/HHA/.


Higher monodromy

Higher monodromy

Pietro Polesello and Ingo Waschkies

For a given category $\catc$ and a topological space $X$, the constant stack on $X$ with stalk $\catc$ is the stack of locally constant sheaves with values in $\catc$. Its global objects are classified by their monodromy, a functor from the fundamental groupoid $\Pi_1(X)$ to $\catc$. 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 $\Catc$ as a 2-functor from the homotopy 2-groupoid $\Pi_2(X)$ to $\Catc$. 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.


Homology, Homotopy and Applications, Vol. 7(2005), No. 1, pp. 109-150

http://www.rmi.acnet.ge/hha/volumes/2005/n1a7/v7n1a7.dvi (ps, dvi.gz, ps.gz, pdf)
ftp://ftp.rmi.acnet.ge/pub/hha/volumes/2005/n1a7/v7n1a7.dvi (ps, dvi.gz, ps.gz, pdf)