Characterizing maximal compact subgroups |
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Authors: | Email author" target="_blank">Sergey?A?AntonyanEmail author |
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Institution: | 1.Departamento de Matemáticas, Facultad de Ciencias,Universidad Nacional Autónoma de México,México Distrito Federal,Mexico |
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Abstract: | 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 \mathbbQ{\mathbb{Q}} -acyclic and \mathbbZ/2\mathbbZ{\mathbb{Z}/2\mathbb{Z}} -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. |
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