On displaceability of pre-Lagrangians in toric contact manifolds
 
 
Description: 

In symplectic geometry one can observe a rigidity of intersections: certain (Lagrangian) submanifolds are forced to intersect each other in more points than an argument from algebraic or differential topology would predict. For example, every compact symplectic toric manifold contains a non-displaceable (i.e. one that cannot be made disjoint from itself by the means of a Hamiltonian isotopy) Lagrangian toric fiber.

In contact geometry, pre-Lagrangians play a related role. We define this notion and explore the question of displaceability of pre-Lagrangian toric fibers in toric contact manifolds. We obtain some results complementary to the symplectic rigidity case. They seem to be linked to orderability and the freeness of the toric action in some not yet fully understood way. In particular, the non-orderable contact toric manifolds S^{2d-1}, S^1 x S^{2d}, d>1, have all their pre-Lagrangian toric fibers displaceable, while the co-sphere bundles T^d \times S^{d-1}, d>1, equipped with a free toric action, have all their pre-Lagrangian toric fibers non-displaceable. We discuss possible generalizations of these examples.In the talk I will mention results from a joint work with Aleksandra Marinkovic.

Date:  2015-07-02
Start Time:   14:30
Speaker:  Milena Pabiniak (IST Lisboa)
Institution:  Instituto Superior Técnico, Lisboa
Place:  Sala 5.5
Research Groups: -Geometry
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