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Albrecht Brehm

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

Universität Rostock, 2019

Abstract: 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 of finite index its fundamental domain D 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.

doctoral thesis   free access