Electronic Communications in Probability

A heat flow approach to the Godbillon-Vey class

Diego S. Ledesma

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We give a heat flow derivation for the Godbillon Vey class. In particular we prove that if $(M,g)$ is a compact Riemannian manifold with a codimension 1 foliation $\mathcal{F} $, defined by an integrable 1-form $\omega $ such that $||\omega ||=1$, then the Godbillon-Vey class can be written as $[-\mathcal{A} \omega \wedge d\omega ]_{dR}$ for an operator $\mathcal{A} :\Omega ^*(M)\rightarrow \Omega ^*(M)$ induced by the heat flow.

Article information

Electron. Commun. Probab., Volume 22 (2017), paper no. 2, 6 pp.

Received: 2 October 2014
Accepted: 28 June 2015
First available in Project Euclid: 5 January 2017

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Zentralblatt MATH identifier

Primary: 58J65: Diffusion processes and stochastic analysis on manifolds [See also 35R60, 60H10, 60J60] 53C12: Foliations (differential geometric aspects) [See also 57R30, 57R32]
Secondary: 60H30: Applications of stochastic analysis (to PDE, etc.) 60J60: Diffusion processes [See also 58J65]

foliation diffusion process stochastic calculus

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Ledesma, Diego S. A heat flow approach to the Godbillon-Vey class. Electron. Commun. Probab. 22 (2017), paper no. 2, 6 pp. doi:10.1214/16-ECP3836. https://projecteuclid.org/euclid.ecp/1483585771

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