First we show that, associated to any Poisson vector field E on a Poisson manifold (M,p), there is a canonical Lie algebroid structure on the first jet bundle J1M which, depends only on the cohomology class of E. We then introduce the notion of a cosymplectic groupoid and we discuss the integrability of the first jet bundle into a cosymplectic groupoid. Finally, we give applications to Atiyah classes and L∞-Algebras.
|International Journal of Geometric Methods in Modern Physics
|Published - Mar 1 2016
All Science Journal Classification (ASJC) codes
- Physics and Astronomy (miscellaneous)