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arXiv · 1309.6156

Jacobi structures and Spencer operators

Marius Crainic·Maria Amelia Salazar
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Abstract

This paper explains the fundamental relation between Jacobi structures and the classical Spencer operator coming from the theory of PDEs so as to provide a direct and geometric approach to the integrability of Jacobi structures. It uses recent results on the integrability of Spencer operators and multliplicative forms on Lie groupoids with non-trivial coefficients. In Theorem 1 we show that the Spencer operator associated to a contact groupoid reveals that the base manifold carries a Jacobi structure. Theorem 2 deals with the problem of integrating Jacobi structures to contact groupoids.

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Marius Crainic, Maria Amelia Salazar. 2014-04-27. Jacobi structures and Spencer operators. https://arxiv.org/abs/1309.6156

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