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arXiv · 1709.09728

Covering Groups of Nonconnected Topological Groups and 2-Groups

Dmitriy Rumynin·Demyan Vakhrameev·Matthew Westaway
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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 inverse of each other.

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Dmitriy Rumynin, Demyan Vakhrameev, Matthew Westaway. 2017-09-27. Covering Groups of Nonconnected Topological Groups and 2-Groups. https://arxiv.org/abs/1709.09728

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