MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Covering group theory for topological groups

Valerii N. Berestovskii and Conrad Plaut


We develop a covering group theory for a large category of "coverable" topological groups, which includes all metrizable, connected, locally connected groups, and even many totally disconnected groups. Our covering group theory produces a categorial notion of fundamental group. In contrast to the traditional theory, our fundamental group is a naturally a topological group, and is the inverse limit of discrete groups. Our work also reveals a link between the fundamental group and global extension properties of local group homomorphisms. We provide methods for computing the fundamental group of inverse limits and dense subgroups or completions of coverable groups. The paper includes a number of examples and open problems.

MSC Codes:
22A05, 22D05
topological group, universal covering group, fundamental group

Related publications

2001 Repository Open Access
Valerii N. Berestovskii and Conrad Plaut

Covering group theory for topological groups

In: Topology and its applications, 114 (2001) 2, pp. 141-186