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. 1057–1068DOI 10.2977/PRIMS/1231263779