Jacobi structures and Spencer operators
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.
Keywords
Cite
@article{arxiv.1309.6156,
title = {Jacobi structures and Spencer operators},
author = {Marius Crainic and Maria Amelia Salazar},
journal= {arXiv preprint arXiv:1309.6156},
year = {2014}
}
Comments
This is a revised version (where a new chapter on "Jacobi structures and their associated Spencer operator" appeared) to appear in Journal de Math\'ematiques Pures et Appliqu\'ees