Open Access
2017 A heat flow approach to the Godbillon-Vey class
Diego S. Ledesma
Electron. Commun. Probab. 22: 1-6 (2017). DOI: 10.1214/16-ECP3836


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.


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Diego S. Ledesma. "A heat flow approach to the Godbillon-Vey class." Electron. Commun. Probab. 22 1 - 6, 2017.


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

zbMATH: 1358.58016
MathSciNet: MR3607797
Digital Object Identifier: 10.1214/16-ECP3836

Primary: 53C12 , 58J65
Secondary: 60H30 , 60J60

Keywords: diffusion process , Foliation , stochastic calculus

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