Journal of the Mathematical Society of Japan

On commutators of foliation preserving homeomorphisms

Kazuhiko FUKUI and Hideki IMANISHI

Full-text: Open access

Abstract

We consider the group of foliation preserving homeomorphisms of afoliated 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.

Article information

Source
J. Math. Soc. Japan, Volume 51, Number 1 (1999), 227-236.

Dates
First available in Project Euclid: 10 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1213108359

Digital Object Identifier
doi:10.2969/jmsj/05110227

Mathematical Reviews number (MathSciNet)
MR1661044

Zentralblatt MATH identifier
0928.57034

Subjects
Primary: 57R30: Foliations; geometric theory

Keywords
Commutator homology perfect homeomorphisms foliation

Citation

FUKUI, Kazuhiko; IMANISHI, Hideki. On commutators of foliation preserving homeomorphisms. J. Math. Soc. Japan 51 (1999), no. 1, 227--236. doi:10.2969/jmsj/05110227. https://projecteuclid.org/euclid.jmsj/1213108359


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