Covering groups of non-connected topological groups revisited

Details Covering groups of non-connected topological groups revisited Covering groups of non-connected topological groups revisited

2000-09-02

arxiv.org/abs/math/0009021v2

Math. Proc. Camb. Phil. Soc. 115 (1994) 97-110

Mathematics

Algebraic Topology

13 pages, A4, Paul Taylors' diagrams. archived here for availability Some improvements to diagrams and new and updated referen

Scientific paper

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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