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Elke Enning

Milena Pabinik: Rigidity in contact geometry and symplectic geometry. Auf diesen Vortrag wird besonders hingewiesen.

Wednesday, 02.11.2016 11:00 im Raum M6

Mathematik und Informatik

Symplectic manifolds, i.e. manifolds with closed, non-degenerate 2-forms, posses certain rigidity proper-ties (symplectic camel, Gromov non-squeezing theorem). An important manifestation of rigidity is given by the conjectures posed by V. Arnold describing a lower bound for the number of fixed points of a (Ham-iltonian) diffeomorphism h of a compact symplectic manifold and a lower bound for the number of inter-section points of certain half-dimensional subsets L with their images h(L). These lower bounds are great-er than what topological arguments could predict. Translating these notions to the setting of contact manifolds (manifolds with completely non-integrable hyperplane distribution) one is looking for lower bounds of translated points of a (contact Hamiltonian) diffeomorphism and for non-displaceable pre-Lagrangian submanifolds. In this talk I will discuss the above rigidity properties for contact and symplectic manifolds equipped with a toric action. In particular, I will compare the non-displaceability properties of toric orbits in symplectic and contact setting (based on a work with A. Marinkovic). We will see arguments suggesting that the ex-istence of a non-displaceable generic toric orbit in the contact setting is related to other important proper-ties of contact manifolds, such as orderability and the existence of quasimorphisms. If time permits, I will explain how a toric action could be used to generalize the construction of a quasimorphism, (called the non-linear Maslov index), given by Givental for projective spaces, to lens spaces, and further to other prequantizations of symplectic toric manifolds (work in progress with G. Granja, Y. Karshon, S. Sandon).



Angelegt am Tuesday, 25.10.2016 14:35 von Elke Enning
Geändert am Tuesday, 25.10.2016 14:38 von Elke Enning
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