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A heat flow approach to the Godbillon-Vey class. (English) Zbl 1358.58016

Summary: 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.

MSC:

58J65 Diffusion processes and stochastic analysis on manifolds
53C12 Foliations (differential geometric aspects)
60H30 Applications of stochastic analysis (to PDEs, etc.)
60J60 Diffusion processes
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