Fukaya categories of Stein manifolds

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• Mohammed Abouzaid, Clay
• Wednesday 09 May 2012, 16:00-17:00
• MR13.

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

According to Eliashberg and Giroux, the symplectic topology of Stein manifolds can be understood by induction on dimension using Lefschetz fibrations. I will explain joint work with Seidel which yields a formula for the (wrapped) Fukaya categories of such manifolds along the same scheme. The end result is that the Fukaya categories of Stein manifolds are “smooth categories” defined over the integers. I will review the notion of a smooth category, which is the setting of non-commutative geometry in the sense of Kontsevich, and explain how Homological mirror symmetry can be used to relate our formula to ideas in the study of derived categories of coherent sheaves.

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

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