Bicrossed products induced by Poisson vector fields and their integrability (Q2802578)

This paper introduces and studies the notion of cosymplectic groupoid. Let us recall that Lie algebroids are very useful to understand geometric structures on manifolds. In this work, the authors first prove the existence of a canonical Lie algebroid structure naturally associated with any Poisson vector field on a Poisson manifold, which depends only on the cohomology class of the vector field. Then, the notion of cosymplectic groupoid is developed and the integrability of the first jet bundle into a cosymplectic groupoid is investigated. Finally, the authors construct a bicrossed product and apply their construction to obtain results on \(L_\infty\) algebras and Atiyah classes.