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.
Original language | English |
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Journal | Communications in Algebra |
Volume | 47 |
DOIs | |
Publication status | Published - 2 Dec 2019 |
Keywords
- 2-group
- universal cover
- group extension
- cohomology