Central Extensions and Cohomology

2023/07/27 by Pranjal Jain, Rohit Joshi, Joshi, Rohit +2
Mathematics · #22F99 #55R35 #55R37 #Advanced Topics in Algebra #Advanced Topology and Set Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT #msc:22F99 #msc:55R35 #msc:55R37

paper · pdf · doi:10.48550/arxiv.2307.14658

openalex publication_date 2023/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28 · arxiv created 2026/07/31 · arxiv updated 2026/08/03

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, we associate a cohomology class in H²(BG;A). We prove this association is injective, and bijective in many cases. A homomorphism of such groups lifts to a central extension iff the pullback of the associated cohomology class vanishes.

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