TY - JOUR
T1 - Covering groups of nonconnected topological groups and 2-groups
AU - Rumynin, Dmitriy
AU - Vakhrameev, Demyan
AU - Westaway, Matthew
PY - 2019/12/2
Y1 - 2019/12/2
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/85066876193
U2 - 10.1080/00927872.2019.1612425
DO - 10.1080/00927872.2019.1612425
M3 - Article
SN - 0092-7872
VL - 47
SP - 5207
EP - 5217
JO - Communications in Algebra
JF - Communications in Algebra
IS - 12
ER -