Monodromy representations of completed coverings

Abstract

In this paper we consider completed coverings that are branched coverings in the sense of Fox. For completed coverings between PL manifolds we give a characterization of the existence of a monodromy representation and the existence of a locally compact monodromy representation. These results stem from a characterization of the discreteness of a completed normal covering. We also show that a completed covering admitting a monodromy representation is discrete and that the image of the branch set is closed.