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Algebra/Topology Seminar – Orsola-Capovilla Searle (UC Davis)

November 10, 2021 @ 11:00 am - 12:00 pm

Title: Infinitely many Lagrangian Tori in Milnor fibers constructed via Lagrangian Fillings of Legendrian links

Abstract: One approach to studying symplectic manifolds with contact boundary is to consider Lagrangian submanifolds with Legendrian boundary; in particular, one can study exact Lagrangian fillings of Legendrian links. There are still many open questions on the spaces of exact Lagrangian fillings of Legendrian links in the standard contact 3-sphere, and one can use Floer theoretic invariants to study such fillings. We show that a family of oriented Legendrian links has infinitely many distinct exact orientable Lagrangian fillings up to Hamiltonian isotopy. Within this family, we provide some of the first examples of a Legendrian link that admits infinitely many planar exact Lagrangian fillings. Weinstein domains are examples of symplectic manifolds with contact boundary that have a handle decomposition compatible with the symplectic structure of the manifold. Weinstein handlebody diagrams are given by projections of Legendrian submanifolds. We provide Weinstein handlebody diagrams of the 4-dimensional Milnor fibers of T_{p,q,r} singularities, which we then use to construct infinitely many Lagrangian tori and spheres in these spaces.


November 10, 2021
11:00 am - 12:00 pm
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