English

Crossed modules and symmetric cohomology of groups

K-Theory and Homology 2019-02-07 v1 Algebraic Topology

Abstract

This paper links the third symmetric cohomology (introduced by Staic and Zarelua ) to crossed modules with certain properties. The equivalent result in the language of 2-groups states that an extension of 2-groups corresponds to an element of HS3HS^3 iff it possesses a section which preserves inverses in the 2-categorical sense. This ties in with Staic's (and Zarelua's) result regarding HS2HS^2 and abelian extensions of groups.

Keywords

Cite

@article{arxiv.1902.01900,
  title  = {Crossed modules and symmetric cohomology of groups},
  author = {Mariam Pirashvili},
  journal= {arXiv preprint arXiv:1902.01900},
  year   = {2019}
}