Tohoku Mathematical Journal
2009
September
SECOND SERIES VOL. 61, NO. 3

Tohoku Math. J.
61 (2009), 393-416

Title INFINITESIMAL DERIVATIVE OF THE BOTT CLASS AND THE SCHWARZIAN DERIVATIVES

Author Taro Asuke

(Received December 26, 2007, revised January 26, 2009)
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.

2000 Mathematics Subject Classification. Primary 58H10; Secondary 32S65, 53B10.
Key words and phrases. Infinitesimal deformations, Bott class, Schwarzian derivatives.

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