On commutators of foliation preserving homeomorphisms

Kazuhiko FUKUI; Hideki IMANISHI

doi:10.2969/jmsj/05110227

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January, 1999 On commutators of foliation preserving homeomorphisms

Kazuhiko FUKUI, Hideki IMANISHI

J. Math. Soc. Japan 51(1): 227-236 (January, 1999). DOI: 10.2969/jmsj/05110227

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.

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Kazuhiko FUKUI. Hideki IMANISHI. "On commutators of foliation preserving homeomorphisms." J. Math. Soc. Japan 51 (1) 227 - 236, January, 1999. https://doi.org/10.2969/jmsj/05110227