### Mathematisch-Naturwissenschaftliche Fakultät

## Institut für Mathematik

### Fachgebiet: Algebra

Betreuer: Prof. Dr. Jan-Christoph Schlage-Puchta

**Dipl. -Math.** **Albrecht** **Brehm**

(e-mail: albrecht.brehm@uni-rostock.de )

*On the geometry of finite index subgroups of groups acting properly on locally finite trees and polyhedral complexes*

Let G be a group acting properly on a simply connected manifold.
There is a fundamental domain DG for that action. The map, which
assigns to each subgroup Δ of finite index its fundamental domain DΔ
yields a correspondence between coverings of DG of finite degree and
finite index subgroups of G. We are interested in the question how the
branching points behave under the transition from DG to its finite
covers. This work presents an approach which allows to solve such
questions in a purely group theoretical framework. This approach is
applied to a concrete example.