On the structure of the group of Lipschitz homeomorphisms and its subgroups

Abstract

We consider the group of Lipschitz homeomorphisms of a Lipschitz manifold and its subgroups. First we study properties of Lipschitz homeomorphisms and show the local contractibility and the perfectness of the group of Lipschitz homeo-morphisms. Next using this result we can prove that the identity component of the group of equivariant Lipschitz homeomorphisms of a principal G-bundle over a closed Lipschitz manifold is perfect when G is a compact Lie group.