On symplectic stabilisations and mapping classes

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• Ailsa Keating, Cambridge
• Wednesday 14 February 2018, 16:00-17:00
• MR13.

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

In real dimension two, the symplectic mapping class group of a surface agrees with its `classical’ mapping class group, whose properties are well-understood. To what extend do these generalise to higher-dimensions? We consider specific pairs of symplectic manifolds (S, M), where S is a surface, together with collections of Lagrangian spheres in S and in M, say v_1, ...,v_k and V_1, ...,V_k, that have analogous intersection patterns, in a sense that we will make precise. Our main theorem is that any relation between the Dehn twists in the V_i must also hold between Dehn twists in the v_i. Time allowing, we will give some corollaries, such as embeddings of certain interesting groups into auto-equivalence groups of Fukaya categories.

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

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