MIT Geometry and Topology Seminar

Monday, May 15, 2023 at 3:00pm

Building 2, 2-449

Speaker: Abigail Ward

Title: Arborealization and the construction of Floer homotopy types for Weinstein manifolds

Abstract: One of the aims of Floer homotopy theory is to produce refined Floer-theoretic invariants, called Floer homotopy types, of symplectic manifolds; for example, in 2007 Cohen showed that one can recover the suspension spectrum of the free loop space of a manifold M from the Hamiltonian Floer theory of T^*M, strengthening Viterbo's result that H^*(LM) and HF^*(T^*M) are isomorphic. Weinstein manifolds form a class of open symplectic manifolds which generalize cotangent bundles, and it is a natural question to ask when Floer homotopy types exist for such manifolds. Arborealizable Weinstein manifolds are a subclass of Weinstein manifolds which retract onto Lagrangian skeleta with particularly simple singularities that can be described combinatorially. We explore the relationship between the arborealizability of a Weinstein manifold X and the topological conditions that allow one to construct a Floer homotopy type for X. This is joint work in progress with Daniel Álvarez-Gavela and Tim Large.

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