On commutators of foliation preserving Lipschitz homeomorphisms

Abstract

We consider the group of foliation preserving Lipschitz homeomorphisms of a Lipschitz foliated manifold. First we show that the identity component of the group of leaf preserving Lipschitz homeomorphisms of a Lipschitz foliated manifold is perfect. Next using this result we compute the first homology of the group of foliation preserving Lipschitz homeomorphisms of a codimension one $C^{2}$-foliated manifold. Then we have results which are different from those of topological and differentiable cases.