Tohoku Mathematical Journal

Infinitesimal derivative of the Bott class and the Schwarzian derivatives

Taro Asuke

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Abstract

An infinitesimal derivative of the Bott class is defined by generalizing Heitsch'es construction. We prove a formula relating the infinitesimal derivative to the Schwarzian derivatives, which gives a generalization of the Maszczyk formula for the Godbillon-Vey class of real codimension-one foliations. As an application, a residue of infinitesimal derivatives with respect to the Julia set in the sense of Ghys, Gomez-Mont and Saludes is introduced.

Article information

Source
Tohoku Math. J. (2), Volume 61, Number 3 (2009), 393-416.

Dates
First available in Project Euclid: 16 October 2009

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1255700201

Digital Object Identifier
doi:10.2748/tmj/1255700201

Mathematical Reviews number (MathSciNet)
MR2568261

Zentralblatt MATH identifier
1198.32014

Subjects
Primary: 58H10: Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.) [See also 57R32]
Secondary: 32S65: Singularities of holomorphic vector fields and foliations 53B10: Projective connections

Keywords
Infinitesimal deformations Bott class Schwarzian derivatives

Citation

Asuke, Taro. Infinitesimal derivative of the Bott class and the Schwarzian derivatives. Tohoku Math. J. (2) 61 (2009), no. 3, 393--416. doi:10.2748/tmj/1255700201. https://projecteuclid.org/euclid.tmj/1255700201


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References

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