Floer theoretically essential tori in rational blowdowns

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• Yankl Lekili, Cambridge
• Wednesday 14 March 2012, 16:00-17:30
• MR13.

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

We compute the Floer cohomology of monotone tori in the Stein surface obtained by a linear plumbing of cotangent bundles of spheres, also known as the Milnor fibre associated with the complex surface singularity of type A-n. We next study some finite quotients of the A-n Milnor fibre which coincide with the Stein surfaces that appear in Fintushel and Stern’s rational blowdown construction. We show that these Stein surfaces have no exact Lagrangian submanifolds by using the already available and in depth understanding of the Fukaya category of the A-n Milnor fibre coming from homological mirror symmetry. On the contrary, we find Floer theoretically essential monotone Lagrangian tori, finitely covered by the monotone tori that we studied in the A-n Milnor fibre. We conclude that these Stein surfaces have non-vanishing symplectic cohomology. Joint work with Maksim Maydanskiy.

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

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