Vol. 39, No. 1, 1971

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Extensions of topological groups

Lawrence Gerald Brown

Vol. 39 (1971), No. 1, 71–78

In this paper, we will be concerned with topological group extensions of a polonais group A by a polonais group G. When A is abelian, we will consider two cohomology groups: H2(G,A) and HV 2(G,A).H2(G,A) is based on Borel cochains and was studied by Moore. HV 2(G,A) is obtained by identifying cochains which differ only on a first category set, an idea suggested to us by D. Wigner. We will show that each of the groups classifies the extensions and that the hypothesis that A be abelian can be eliminated.

Mathematical Subject Classification 2000
Primary: 57F99
Secondary: 22A25, 22D10
Received: 2 November 1970
Published: 1 October 1971
Lawrence Gerald Brown