Weak extension theorem for measure-preserving homeomorphisms of noncompact manifolds

TL;DR

This paper introduces a weak extension property for embeddings from group actions and demonstrates its application to measure-preserving homeomorphisms on noncompact manifolds, showing local contractibility of these groups.

Contribution

It establishes a weak extension theorem for measure-preserving homeomorphisms on noncompact manifolds, advancing understanding of their topological properties.

Findings

Weak extension theorems for measure-preserving homeomorphisms

Local contractibility of the homeomorphism group with compact support

Introduction of a general weak extension property for group actions

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.