Tohoku Mathematical Journal

Notes on 'Infinitesimal derivative of the Bott class and the Schwarzian derivatives'

Taro Asuke

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Abstract

The derivatives of the Bott class and those of the Godbillon-Vey class with respect to infinitesimal deformations of foliations, called infinitesimal derivatives, are known to be represented by a formula in the projective Schwarzian derivatives of holonomies [3], [1]. It is recently shown that these infinitesimal derivatives are represented by means of coefficients of transverse Thomas-Whitehead projective connections [2]. We will show that the formula can be also deduced from the latter representation.

Article information

Source
Tohoku Math. J. (2), Volume 69, Number 1 (2017), 129-139.

Dates
First available in Project Euclid: 26 April 2017

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1493172132

Digital Object Identifier
doi:10.2748/tmj/1493172132

Mathematical Reviews number (MathSciNet)
MR3640018

Zentralblatt MATH identifier
06726845

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 58H15: Deformations of structures [See also 32Gxx, 58J10] 53C12: Foliations (differential geometric aspects) [See also 57R30, 57R32] 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)

Keywords
Foliations characteristic classes deformations

Citation

Asuke, Taro. Notes on 'Infinitesimal derivative of the Bott class and the Schwarzian derivatives'. Tohoku Math. J. (2) 69 (2017), no. 1, 129--139. doi:10.2748/tmj/1493172132. https://projecteuclid.org/euclid.tmj/1493172132


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References

  • T. Asuke, Infinitesimal derivative of the Bott class and the Schwarzian derivatives, Tohoku Math. J. (2) 61 (2009), 393–416.
  • T. Asuke, Transverse projective structures of foliations and infinitesimal derivatives of the Godbillon-Vey class, Internat. J. Math. 26 (2015), 1540001, 29pp.
  • T. Maszczyk, Foliations with rigid Godbillon-Vey class, Math. Z. 230 (1999), 329–344.
  • T. Mizutani, The Godbillon-Vey cocycle of $\mathrm{Diff} \mathbb{R}^n$, A fête of Topology: papers dedicated to Itiro Tamura, pp. 49–62, Academic Press, Boston, MA, 1988.