On commutators of foliation preserving homeomorphisms. (English) Zbl 0928.57034

Fukui, Kazuhiko; Imanishi, Hideki

J. Math. Soc. Japan 51, No. 1, 227-236 (1999).

The authors compute the first homologies of the group of foliation preserving homeomorphisms for codimension one foliations. They 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.

Reviewer: Andrzej Piatkowski (Łódź)

MSC:

57R30

Foliations in differential topology; geometric theory

Keywords:

commutator; group of foliation preserving homeomorphisms; codimension one foliations