Central Extensions and Cohomology
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929261796917248 |
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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 |