Covering groups of non-connected topological groups revisited

R. Brown; O. Mucuk

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Covering groups of non-connected topological groups revisited

R. Brown·O. Mucuk

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Abstract

In general a universal covering of a non connected topological group need not admit a topological group structure such that the covering map is a morphism of topological groups. This result is due to R.L. Taylor (1953). We generalise this result and relate it to the theory of obstructions to group extensions. The methods use: the equivalence between covering maps of X and covering groupoids of the fundamental groupoid of X; the equivalence between group groupoids and crossed modules; and descriptions of cohomology in terms of crossed complexes.

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R. Brown, O. Mucuk. 2006-12-18. Covering groups of non-connected topological groups revisited. https://arxiv.org/abs/math/0009021

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