Characterizing maximal compact subgroups

We prove that for a compact subgroup H of a locally compact almost connected group G , the following properties are mutually equivalent: (1) H is a maximal compact subgroup of G , (2) the coset space G / H is -acyclic and -acyclic in Čech cohomology, (3) G / H is contractible, (4) G / H is homeomorp...

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Bibliographic Details
Published in:Archiv der Mathematik 2012-06, Vol.98 (6), p.555-560
Main Author: Antonyan, Sergey A.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:We prove that for a compact subgroup H of a locally compact almost connected group G , the following properties are mutually equivalent: (1) H is a maximal compact subgroup of G , (2) the coset space G / H is -acyclic and -acyclic in Čech cohomology, (3) G / H is contractible, (4) G / H is homeomorphic to a Euclidean space, (5) G / H is an absolute extensor for paracompact spaces, (6) G / H is a G -equivariant absolute extensor for paracompact proper G -spaces having a paracompact orbit space.
ISSN:0003-889X
1420-8938
DOI:10.1007/s00013-012-0389-8