An Algorithmic Approach to Fundamental Groups and Covers ofCombinatorial Cell Complexes

Sarah Rees and Leonard H. Soicher


homotopy invariants, fundamental group, covers, simplicial complexes, incident geometries, graphs, algorithms


In Journal of Symbolic Computation 29 (2000) 59-77


We first 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, first homology groups, deck groups, and covers of finite simple such complexes. In the case of clique complexes of finite simple graphs, the algorithms described have been implemented in {\sf GAP}, making use of the {\sf GRAPE} package. \

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Alternatively, you can request a copy by e-mailing me.

Sarah Rees
22nd August 1999