An Algorithmic Approach to Fundamental Groups and Covers of Combinatorial Cell Complexes

We rst develop a construction, originally due to Reidemeister, of the fundamental group and covers of a combinatorial cell complex. Then, we describe a practical algorithmic approach to the computation of fundamental groups, rst homology groups, deck groups, and covers of nite simple such complexes. In the case of clique complexes of nite simple graphs, the algorithms described have been implemented in GAP, making use of the GRAPE package. Acknowledgements We thank Klaus Lux, Armando Martino and Martin Roller for very helpful discussions during the preparation of this paper.