Locally continuously perfect groups of homeomorphisms

TL;DR

This paper introduces the concept of locally continuously perfect groups, generalizes previous notions, and proves that the identity component of the homeomorphism group of a manifold is locally continuously perfect.

Contribution

It defines locally continuously perfect groups and establishes that the identity component of homeomorphism groups of manifolds possesses this property.

Findings

The identity component of the homeomorphism group of a manifold is locally continuously perfect.

The notion of locally continuously perfect groups generalizes locally smoothly perfect groups.

Examples include equivariant homeomorphism groups.

Abstract

The notion of a locally continuously perfect group is introduced and studied. This notion generalizes locally smoothly perfect groups introduced by Haller and Teichmann. Next, we prove that the path connected identity component of the group of all homeomorphisms of a manifold is locally continuously perfect. The case of equivariant homeomorphism group and other examples are also considered.