Семинар за симплектичку топологију, 11. јун 2024.

• 10. Јун, 2024
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Наредни састанак Семинара за симплектичку топологију биће одржан у уторак, 11. јуна 2024, у сали 840 Математичког факултета са почетком у 17 часова.

Предавач: Frol Zapoljski

Наслов предавања: ON THE CONTACT MAPPING CLASS GROUP OF THE CONTACTIZATION OF MILNORʼS A_m-FIBERS

Апстракт:
The symplectic isotopy problem for a given symplectic manifold is determining which symplectomorphisms are smoothly isotopic to the identity, but not through symplectomorphisms. Equivalently, this problem concerns the size of the kernel of the natural homomorphism from the symplectic mapping class group to its smooth counterpart. An analogous problem can be posed for a given contact manifold. On the symplectic side, a beautiful construction due to Khovanov-Seidel yields an embedding of the braid group on m+1 strands into the symplectic mapping class group of Milnorʼs A_m-fiber, which is a certain smooth affine variety in any complex dimension at least 2. Moreover, they show that the aforementioned kernel is always large, with its size depending on the dimension. On the contact side we consider the contactization of the Milnor fiber, and show that the composition of the Khovanov-Seidel embedding with a natural lifting homomorphism from the symplectic mapping class group of the fiber to the contact mapping class group of its contactization is injective. In particular, we obtain large subgroups of the contact mapping class group which are smoothly trivial. The proof uses a partially linearized version of the Chekanov-Eliashberg Legendrian contact homology for two-component Legendrian links. Joint work with Sergei Lanzat.