English

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