Integrating Lie algebroids via stacks and applications to Jacobi manifolds

Details Integrating Lie algebroids via stacks and applications to Jacobi manifolds Integrating Lie algebroids via stacks and applications to Jacobi manifolds

2005-05-09

arxiv.org/abs/math/0505158v1

Mathematics

Differential Geometry

Ph. D. thesis, 2004, U.C. Berkeley; references edited

Scientific paper

Lie algebroids can not always be integrated into Lie groupoids. We introduce a new object--``Weinstein groupoid'', which is a differentiable stack with groupoid-like axioms. With it, we have solved the integration problem of Lie algebroids. It turns out that every Weinstein groupoid has a Lie algebroid, and every Lie algebroid can be integrated into a Weinstein groupoid. Furthermore, we apply this general result to Jacobi manifolds and construct contact groupoids for Jacobi manifolds. There are further applications in prequantization and integrability of Poisson bivectors.

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