# Covering groups of nonconnected topological groups and 2-groups

@article{Rumynin2019CoveringGO, title={Covering groups of nonconnected topological groups and 2-groups}, author={Dmitriy Rumynin and Demyan Vakhrameev and Matthew Westaway}, journal={Communications in Algebra}, year={2019}, volume={47}, pages={5207 - 5217} }

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.

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This paper is a fundamental study of the Real $2$-representation theory of $2$-groups. It also contains many new results in the ordinary (non-Real) case. Our framework relies on a $2$-equivariant… Expand

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