Camilo Angulo (Universität Göttingen)
Poisson geometry lies in the intersection of symplectic geometry, foliation theory and Lie theory. As in each of these areas compactness hypotheses yield a wealth of results, it would be desirable to have a notion of compactness in Poisson geometry that simultaneously subsumes the theory of compact semisimple compact Lie groups and compact symplectic manifolds. This goal has been recently achieved by Crainic, Fernandes and Martinez-Torres, who defined a Poisson manifold of compact type (PMCTs) to be a Poisson manifold whose integrating symplectic groupoid is proper. The wonderful properties of these PMCTs lie in contrast to their relative scarcity. The geometric and topological constraints that go into building a PMCT make their definition rather demanding, and in so, constructing a PMCT beyond the trivial case of a compact symplectic manifold with finite fundamental group has proven a challenging problem. In this talk, after properly explaining the elements that go into play, we explain how by allowing for other geometric structures to "integrate" Poisson manifolds, one can get more examples while preserving most of the compactness properties.
For more information and log in details please contact Christian Molle.
