R. Brown,  E. J. Moore, T. Porter,  C. D. Wensley

Crossed Complexes, and Free Crossed Resolutions for Amalgamated Sums and HNN-Extensions of Groups

The category of crossed complexes gives an algebraic model of CW-complexes and cellular maps. Free crossed resolutions of groups contain information on a presentation of the group as well as higher homological information. We relate this to the problem of calculating non-abelian extensions. We show how the strong properties of this category allow for the computation of free crossed resolutions for amalgamated sums and HNN-extensions of groups, and so obtain computations of higher homotopical syzygies in these cases.