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

Ronald Brown; Emma J. Moore; Timothy Porter; Christopher D. Wensley

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

Ronald Brown·Emma J. Moore·Timothy Porter·Christopher D. Wensley

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Abstract

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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Ronald Brown, Emma J. Moore, Timothy Porter, Christopher D. Wensley. 2002-07-03. Crossed complexes, and free crossed resolutions for amalgamated sums and HNN-extensions of groups. https://arxiv.org/abs/math/0207037

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