On Poisson manifolds that can be embedded into rigid Poisson manifolds (Ioan Marcut) скачать в хорошем качестве

On Poisson manifolds that can be embedded into rigid Poisson manifolds (Ioan Marcut)

Ioan Marcut (University of Illinois at Urbana-Champaign) Monday, August 4, 2014 Conn's linearization theorem has always been regard as a manifestation of a rigidity phenomenon of the Lie-Poisson structure of a compact semi-simple Lie algebra. This was explained by the rigidity theorem, which gives the following sucient condition for a Poisson structure to have no deformations: integrability by a symplectic groupoid whose source bers are 1-connected, compact and have no second cohomology; such Poisson structures I call "rigid". Besides Conn's theorem, the rigidity result implies also the normal form theorem around symplectic leaves. Less expected are the applications of the rigidity theorem to deformation theory. Namely, the deformations of the Poisson structure on a compact saturated submanifold of a rigid Poisson manifold can be realized geometrically by nearby saturated submanifolds. This motivates the search for an intrinsic description of the Poisson manifolds that are embeddable into rigid Poisson manifolds, which I will explain in the talk, among other interesting properties of this natural class of Poisson structures.