Covering group theory for locally compact groups

Abstract

In an earlier paper we introduced a covering group theory for a category of “coverable” topological groups, including a generalized notion of universal cover. In this paper we characterize coverable locally compact groups. As an application we show that the classical covering group theories of Poincaré and Chevalley, as well as a variants due to Tits and Hofmann–Morris, are all equivalent for locally compact groups, and are strictly special cases of our theory (which does not require any form of local simple connectivity). As a second application we show the existence of an inverse sequence of locally compact groups, whose bonding homomorphisms are open surjections with discrete kernel, such that the natural projections from the inverse limit are not surjective.