Characterizing maximal compact subgroups

摘要

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 ?/2?-acyclic in ?ech 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.