Arborealization and the construction of Floer homotopy types for Weinstein manifolds

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• Abigail Ward (Cambridge)
• Wednesday 15 November 2023, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Oscar Randal-Williams.

Weinstein manifolds are open symplectic manifolds which behave like cotangent bundles in that they retract onto singular Lagrangian skeleta; a Weinstein manifold is said to be arborealizable if the retraction can be chosen so that the singularities of the resulting skeleton are all particularly simple (or arboreal). We explore the relationship between the arborealizability of a Weinstein manifold X and the topological conditions that allow one to construct Floer homotopy types associated to the symplectic invariants of X. We prove some partial results, and in particular we show that any arborealizable Weinstein manifold satisfying 2c_1(X)=0 has Floer-theoretic invariants which can be defined over the sphere spectrum. This is joint work in progress with Daniel Álvarez-Gavela and Tim Large.

This talk is part of the Differential Geometry and Topology Seminar series.

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