On commutators of foliation preserving homeomorphisms

Dedicated to Professor Hiroyasu Ishimoto on his 60th birthday

Abstract

We consider the group of foliation preserving homeomorphisms of a foliated manifold. We compute the first homologies of the groups for codimension one foliations. Especially, we show that the group for the Reeb foliation on the 3-sphere is perfect and the groups for irrational linear foliations on the torus are not perfect.