JournalsprimsVol. 44, No. 4pp. 1057–1068

On the First Homology of the Groups of Foliation Preserving Diffeomorphisms for Foliations with Singularities of Morse Type

  • Kazuhiko Fukui

    Kyoto Sangyo University, Japan
On the First Homology of the Groups of Foliation Preserving Diffeomorphisms for Foliations with Singularities of Morse Type cover

Abstract

Let ℚ_n_ be an n-dimensional Euclidean space and ℱφ be the foliation defined by levels of a Morse function φ : ℚn → ℚ. We determine the first homology of the identity component of the foliation preserving diffeomorphism group of (ℚn , ℱφ). Then we can apply it to the calculation of the first homology of the foliation preserving diffeomorphism groups for codimension one compact foliations with singularities of Morse type.

Cite this article

Kazuhiko Fukui, On the First Homology of the Groups of Foliation Preserving Diffeomorphisms for Foliations with Singularities of Morse Type. Publ. Res. Inst. Math. Sci. 44 (2008), no. 4, pp. 1057–1068

DOI 10.2977/PRIMS/1231263779