English

Central Extensions and Cohomology

Algebraic Topology 2024-03-05 v2

Abstract

Let G be a group which is topologically a CW-complex, BG a classifying space for G, and A a discrete abelian group. To a central extension of G by A, one can associate a cohomology class in H2(BG,A)H^2(BG,A). We show this association is injective, and bijective in many cases. A homomorphism to G lifts to the extension iff the pullback of the associated cohomology class vanishes.

Keywords

Cite

@article{arxiv.2307.14658,
  title  = {Central Extensions and Cohomology},
  author = {Rohit Joshi and Steven Spallone},
  journal= {arXiv preprint arXiv:2307.14658},
  year   = {2024}
}
R2 v1 2026-06-28T11:41:32.629Z