English

On the second cohomology group of a simplicial group

Algebraic Topology 2011-03-31 v2 K-Theory and Homology

Abstract

We give an algebraic proof for the result of Eilenberg and Mac Lane that the second cohomology group of a simplicial group G can be computed as a quotient of a fibre product involving the first two homotopy groups and the first Postnikov invariant of G. Our main tool is the theory of crossed module extensions of groups.

Keywords

Cite

@article{arxiv.0911.2864,
  title  = {On the second cohomology group of a simplicial group},
  author = {Sebastian Thomas},
  journal= {arXiv preprint arXiv:0911.2864},
  year   = {2011}
}

Comments

Further references added. This article is an extension of the published version