On commutators of foliation preserving homeomorphisms

• FUKUI Kazuhiko

  Department of Mathematics, Kyoto Sangyo University

• IMANISHI Hideki

  Faculty of Integrated Human Studies, Kyoto University

Bibliographic Information

Other Title

• Dedicated to Professor Hiroyasu Ishimoto on his 60th birthday

Abstract

We consider the group of foliation preserving homeomorphisms of a foliated 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.

Journal

• Journal of the Mathematical Society of Japan

  Journal of the Mathematical Society of Japan 51 (1), 227-236, 1999

  The Mathematical Society of Japan

Keywords

• Commutator
• homology
• perfect
• homeomorphisms
• foliation

Details

• CRID: 1390282680092802944
• NII Article ID: 10002151536
• NII Book ID: AA0070177X
• DOI: 10.2969/jmsj/05110227
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• MRID: 1661044
• NDL BIB ID: 4643340
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I4643340
• Text Lang: en
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed