Covering Groups of Nonconnected Topological Groups and 2-Groups
Quantum Algebra
2019-03-27 v4 Category Theory
Group Theory
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.
Keywords
Cite
@article{arxiv.1709.09728,
title = {Covering Groups of Nonconnected Topological Groups and 2-Groups},
author = {Dmitriy Rumynin and Demyan Vakhrameev and Matthew Westaway},
journal= {arXiv preprint arXiv:1709.09728},
year = {2019}
}
Comments
9 pages. Version 2: historical review added. Version 3 (14 pages): historical review revised, minor corrections elsewhere, some of the results did not make it into the final version. Version 4: final journal version with a slightly different (to Version 3) approach