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Geometry, Symmetry and Physics Seminar

Tropical Fukaya algebras

Sushmita Venugopalan, IMSc Chennai

Location:  Webex - email organizers
Date & time: Thursday, 21 May 2020 at 9:00AM - 10:00AM

A multiple cut operation on a symplectic manifold produces a collection of cut spaces, each containing relative normal crossing divisors. We explore what happens to curve count-based invariants when a collection of cuts is applied to a symplectic manifold. The invariant we consider is the Fukaya algebra of a Lagrangian submanifold that is contained in the complement of relative divisors. The ordinary Fukaya algebra in the unbroken manifold is homotopy equivalent to a `broken Fukaya algebra' whose structure maps count `broken disks' associated to rigid tropical graphs. Via a further degeneration, the broken Fukaya algebra is homotopy equivalent to a `tropical Fukaya algebra' whose structure maps are sums of products over vertices of tropical graphs. This is joint work with Chris Woodward.

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