Exact Calabi-Yau structures and disjoint Lagrangian spheres

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• Yin Li, UCL
• Wednesday 23 October 2019, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Ivan Smith.

An exact CY structure is a special kind of smooth CY structure in the sense of Kontsevich-Vlassopoulos. When the wrapped Fukaya category of a Weinstein manifold admits an exact CY structure, there is an induced cohomology class in its 1st degree S^1-equivariant symplectic cohomology, which, under the marking map, goes to an invertible element in the deg 0 (ordinary) symplectic cohomology. This generalizes the notion of a (quasi-) dilation introduced earlier by Seidel-Solomon. We show that one can define q-intersection numbers between simply-connected Lagrangian submanifolds in Weinstein manifolds with exact CY wrapped Fukaya categories and prove that there can be only finitely many disjoint Lagrangian spheres in these manifolds. The simplest non-trivial example of a Weinstein manifold whose wrapped Fukaya category is exact CY but which does not admit a quasi-dilation is the Milnor fiber of a 3-fold triple point studied previously by Smith-Thomas.

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

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