Fukaya categories of the torus and Dehn surgery on 3-manifolds

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• Yanki Lekili, Cambridge
• Wednesday 09 February 2011, 16:00-17:00
• MR4.

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

In joint work with Tim Perutz, we extend the Heegaard Floer theory of Ozsvath-Szabo to compact 3–manifolds with two boundary components. In the particular case of 3-manifolds bounding the 2-sphere and the 2-torus, the simplest version of this extension takes the form of an A-infinity module over the Fukaya category of a once punctured torus. After giving an overview of this extension, I will show that the A-infinity structures on the graded algebra A underlying the Fukaya category of the punctured 2-torus are governed by just two parameters, extracted from the Hochschild cohomology of A. Finally, I will prove that the dg-categories of sheaves on the Weierstrass family of elliptic curves yield a way to realize all such A-infinity structures. This pins down a complete description of the Fukaya A-infinity algebra of the punctured torus, which is non-formal.

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

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