English

Covering groups of non-connected topological groups revisited

Algebraic Topology 2007-05-23 v2 Category Theory

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.

Keywords

Cite

@article{arxiv.math/0009021,
  title  = {Covering groups of non-connected topological groups revisited},
  author = {R. Brown and O. Mucuk},
  journal= {arXiv preprint arXiv:math/0009021},
  year   = {2007}
}

Comments

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