Weak extension theorem for measure-preserving homeomorphisms of noncompact manifolds

Tatsuhiko Yagasaki

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arXiv · 0904.1264

Weak extension theorem for measure-preserving homeomorphisms of noncompact manifolds

Tatsuhiko Yagasaki

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Abstract

In this paper we introduce a general notion of weak extension property for embeddings induced by a group actions. As an example, for the group H(M, m) of measure-preserving homeomorphisms of a noncompact manifold M, we deduce weak type extension theorems, and as an application we exhibit the local contractibility of the group H_c(M, m) of measure-preserving homeomorphisms with compact support of a noncompact connected manifold M endowed with the Whitney topology.

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Tatsuhiko Yagasaki. 2009-04-08. Weak extension theorem for measure-preserving homeomorphisms of noncompact manifolds. https://arxiv.org/abs/0904.1264

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