Covering groups of nonconnected topological groups and 2-groups

Rumynin, Dmitriy; Vakhrameev, Demyan; Westaway, Matthew

doi:10.1080/00927872.2019.1612425

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Covering groups of nonconnected topological groups and 2-groups

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Rumynin, Dmitriy
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1080/00927872.2019.1612425
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arXiv:1709.09728.pdf
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Rumynin, D., Vakhrameev, D., & Westaway, M. (2019). Covering groups of nonconnected topological groups and 2-groups. Communications in Algebra, 47(12), 5207-5217. doi:10.1080/00927872.2019.1612425.

Cite as: https://hdl.handle.net/21.11116/0000-0006-4107-9

Abstract

We investigate the universal cover of a topological group that is not necessarily connected. Its existence as a topological group is governed by a Taylor cocycle, an obstruction in 3-cohomology. Alternatively, it always exists as a topological 2-group. The splitness of this 2-group is also governed by an obstruction in 3-cohomology, a Sinh cocycle. We give explicit formulas for both obstructions and show that they are equal.