Crossed complexes, and free crossed resolutions for amalgamated sums and HNN-extensions of groups
Algebraic Topology
2021-06-22 v1
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.
Keywords
Cite
@article{arxiv.math/0207037,
title = {Crossed complexes, and free crossed resolutions for amalgamated sums and HNN-extensions of groups},
author = {Ronald Brown and Emma J. Moore and Timothy Porter and Christopher D. Wensley},
journal= {arXiv preprint arXiv:math/0207037},
year = {2021}
}
Comments
24 pages, uses xypic