Central Extensions and Cohomology

Fuente: arXiv
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Main Authors: Joshi, Rohit, Spallone, Steven
Format: Preprint
Published: 2023
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author Joshi, Rohit
Spallone, Steven
author_facet Joshi, Rohit
Spallone, Steven
contents 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 $H^2(BG,A)$. 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.
format Preprint
id arxiv_https___arxiv_org_abs_2307_14658
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Central Extensions and Cohomology
Joshi, Rohit
Spallone, Steven
Algebraic Topology
55R35, 55R37, 22F99
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 $H^2(BG,A)$. 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.
title Central Extensions and Cohomology
topic Algebraic Topology
55R35, 55R37, 22F99
url https://arxiv.org/abs/2307.14658