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 . 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.
Cite
@article{arxiv.2307.14658,
title = {Central Extensions and Cohomology},
author = {Rohit Joshi and Steven Spallone},
journal= {arXiv preprint arXiv:2307.14658},
year = {2024}
}