Groups of measure-preserving homeomorphisms of noncompact 2-manifolds

Tatsuhiko Yagasaki

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Groups of measure-preserving homeomorphisms of noncompact 2-manifolds

Tatsuhiko Yagasaki

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Abstract

Suppose M is a noncompact connected 2-manifold and m is a good Radon measure of M with m(partial M) = 0. Let H(M)_0 denote the identity component of the group of homeomorphisms of M equipped with the compact-open topology and let H(M; m)_0 denote the identity component of the subgroup consisting of m-preserving homeomorphisms of M. We use results of A.Fathi and R.Berlanga to show that H(M; m)_0 is a strong deformation retract of H(M)_0 and classify the topological type of H(M; m)_0.

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Tatsuhiko Yagasaki. 2005-07-16. Groups of measure-preserving homeomorphisms of noncompact 2-manifolds. https://arxiv.org/abs/math/0507328

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