Bundle Structure of the Homeomorphism Groups of Locally Compact Homogeneous Spaces

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  • Bundle Structure of the Homeomorphism G

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The space ℋ(X) of homeomorphisms on a locally compact homogeneous space X with a local cross-section is a bundle space over X. If X is separable metrizable and admits a nontrivial flow in addition, then ℋ(X) is an l2-manifold if and only if X is an ANR and ℋ(X,a) is an l2-manifold, where ℋ(X,a) is the subspace of ℋ(X) consisting of all those which leave a point α of X fixed. If X is a locally connected, compact metrizable homogeneous space that is an ANR and admits a local cross-section and a nontrivial flow, then ℋ(X) is an l2-manifold if and only if ℋ(X-a) is an l2-manifold, where ℋ(X-a) is the space of homeomorphisms on X-a (a∈X).

長崎大学教育学部自然科学研究報告. vol.34, p.1-7; 1983

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