buondì,
vi segnalo due seminari di geometria per la prossima settimana. Ringrazio Paolo Ghiggini per aver invitato entrambi. a presto, Bruno
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MARTEDI' 21 OTTOBRE 2014
SEMINARI DI GEOMETRIA 14:00-15:00, Sala Seminari (Dip. Matematica) When is a Stein manifold merely symplectic? Chris Wendl (University College London)
Abstract: Stein manifolds are objects originating in complex geometry that also naturally carry symplectic structures. In recent years, the study of Stein structures has increasingly been dominated by the question of "rigid vs. flexible": on the flexible side, the so-called "subcritical" Stein manifolds satisfy an h-principle in higher dimensions, so their Stein homotopy type is determined by the homotopy class of the underlying almost complex structure, and all "interesting" invariants of such structures vanish. At the other end of the spectrum, one should expect to find pairs of Stein manifolds that are symplectomorphic but not Stein deformation equivalent, though no examples are yet known. In this talk, I will explain where NOT to look for examples: in complex dimension 2, there is a large class of Stein domains that exist somewhere between rigid and flexible, meaning that while the h-principle does not hold in any strict sense, their Stein deformation type is completely determined by their symplectic deformation type. This result depends on some joint work with Sam Lisi and Jeremy Van Horn-Morris involving the relationship between Stein structures and Lefschetz fibrations, which can sometimes be realised as foliations by J-holomorphic curves.
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MERCOLEDI' 22 OTTOBRE 2014
SEMINARI DI GEOMETRIA 11:00-12:00, Sala Seminari (Dip. Matematica) Subcritical contact surgeries and the topology of symplectic fillings Klaus Niederkrüger (Université de Toulouse)
Abstract: (joint work with P. Ghiggini and C. Wendl) By a result of Eliashberg, every symplectic filling of a three-dimensional contact connected sum is obtained by performing a boundary connected sum on another symplectic filling. I will explain a partial generalization of this result for subcritical contact surgeries in higher dimensions: given any 5-dimensional contact manifold that arises from another contact manifold by subcritical surgery, its belt sphere must be nullhomotopic in any symplectically aspherical filling.