## Journal of the Mathematical Society of Japan

### On the structure of the group of Lipschitz homeomorphisms and its subgroups, II

#### Abstract

We study the structure of the group of Lipschitz homeomorphisms of $\mathbold{R}^{n}$ leaving the origin fixed and the group of equivariant Lipschitz homeomorphisms of $\mathbold{R}^{n}$, and show that they are perfect. Next we apply these results for the groups of Lipschitz homeomorphisms of orbifolds and the groups of foliation preserving Lipschitz homeomorphisms for compact Hausdorff $C^{1}$-foliations.

#### Article information

Source
J. Math. Soc. Japan, Volume 55, Number 4 (2003), 947-956.

Dates
First available in Project Euclid: 3 October 2007

https://projecteuclid.org/euclid.jmsj/1191418758

Digital Object Identifier
doi:10.2969/jmsj/1191418758

Mathematical Reviews number (MathSciNet)
MR2003754

Zentralblatt MATH identifier
1043.58003

#### Citation

ABE, Kōjun; FUKUI, Kazuhiko. On the structure of the group of Lipschitz homeomorphisms and its subgroups, II. J. Math. Soc. Japan 55 (2003), no. 4, 947--956. doi:10.2969/jmsj/1191418758. https://projecteuclid.org/euclid.jmsj/1191418758