Interoperating between computer algebra systems: computing homology of groups with kenzo and GAP

In this paper we report on an experience communicating between the GAP computional algebra system (in particular, its HAP package for homological algebra computations) and the Kenzo computer system for Algebraic Topology. Both systems were made to cooperate through an OpenMath link in order to perform computations in group cohomology. Furthermore, once HAP output is integrated into Kenzo, it can be used to compute more complicated algebraic invariants such as the homology groups of various 2-types.