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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