Crossed complexes, and free crossed resolutions for amalgamated sums and HNN-extensions of groups

Details Crossed complexes, and free crossed resolutions for amalgamated sums and HNN-extensions of groups Crossed complexes, and free crossed resolutions for amalgamated sums and HNN-extensions of groups

2002-07-03

arxiv.org/abs/math/0207037v1

Mathematics

Algebraic Topology

24 pages, uses xypic

Scientific paper

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.

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