Tohoku Mathematical Journal

Infinitesimal derivative of the Bott class and the Schwarzian derivatives

Taro Asuke

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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

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

First available in Project Euclid: 16 October 2009

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Zentralblatt MATH identifier

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

Infinitesimal deformations Bott class Schwarzian derivatives


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.

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