## Journal of Mathematics of Kyoto University

### 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.

#### Article information

Source
J. Math. Kyoto Univ., Volume 41, Number 3 (2001), 507-515.

Dates
First available in Project Euclid: 17 August 2009

https://projecteuclid.org/euclid.kjm/1250517615

Digital Object Identifier
doi:10.1215/kjm/1250517615

Mathematical Reviews number (MathSciNet)
MR1878718

Zentralblatt MATH identifier
1012.58005

#### Citation

Fukui, Kazuhiko; Imanishi, Hideki. On commutators of foliation preserving Lipschitz homeomorphisms. J. Math. Kyoto Univ. 41 (2001), no. 3, 507--515. doi:10.1215/kjm/1250517615. https://projecteuclid.org/euclid.kjm/1250517615