Seminarium "The Trans-Carpathian Seminar on Geometry & Physics"

eneralized complex structures were introduced by Hitchin and further studied by Gualtieri. They encompass symplectic structures and complex structures as extreme cases. In the general case, a generalized complex manifold can be seen as an even dimensional Poisson manifold equipped with additional structures. In the first part of the talk, we will review the definition of generalized complex structures and outline their relation with Poisson geometry, Lie algebroids and Lie groupoids. In the second part of the talk, we will propose “generalized contact bundles” as odd dimensional analogues of generalized complex manifolds. Finally, we will outline the relation between generalized contact bundles and Jacobi manifolds, Lie algebroids and Lie groupoids.