An algorithmic approach to fundamental groups and covers of combinatorial cell complexes

We first develop a construction, originally due to Reidemeister, of the fundamental group and covers of a two-dimensional combinatorial cell complex. Then, we describe a practical algorithmic approach to the computation of fundamental groups and first homology groups las finitely presented groups), of first homology groups mod p las vector spaces), of deck groups las permutation groups), and of covers of finite simple such complexes. In the case of clique complexes of finite simple graphs, the algorithms described have been implemented in GAP; making use of the GRAPE package. (C) 2000 Academic Press.