Advanced Studies in Pure Mathematics

On the Fatou–Julia decomposition of transversally holomorphic foliations of complex codimension one

Taro Asuke

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Abstract

The Fatou–Julia decomposition of complex codimension-one foliations is given by Ghys, Gomez-Mont and Saludes. The Julia sets are expected to play a role of minimal sets of real codimension-one foliations. For example, it is known that the Godbillon–Vey class is trivial if the Julia set is empty. In this paper, we propose another decomposition obtained in a slightly different way and announce some results.

Article information

Source
Singularities — Niigata–Toyama 2007, J.-P. Brasselet, S. Ishii, T. Suwa and M. Vaquie, eds. (Tokyo: Mathematical Society of Japan, 2009), 39-47

Dates
Received: 22 January 2008
First available in Project Euclid: 28 November 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1543448010

Digital Object Identifier
doi:10.2969/aspm/05610039

Mathematical Reviews number (MathSciNet)
MR2604075

Zentralblatt MATH identifier
1198.57019

Subjects
Primary: 57R30: Foliations; geometric theory
Secondary: 58H05: Pseudogroups and differentiable groupoids [See also 22A22, 22E65] 37F75: Holomorphic foliations and vector fields [See also 32M25, 32S65, 34Mxx]

Keywords
Holomorphic foliations Fatou set Julia set Riemannian foliations

Citation

Asuke, Taro. On the Fatou–Julia decomposition of transversally holomorphic foliations of complex codimension one. Singularities — Niigata–Toyama 2007, 39--47, Mathematical Society of Japan, Tokyo, Japan, 2009. doi:10.2969/aspm/05610039. https://projecteuclid.org/euclid.aspm/1543448010


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