## Northern California Symplectic Geometry Seminar: On symplectic stabilisations and mapping classes

Seminar | April 2 | 2:30-3:30 p.m. | 891 Evans Hall

Ailsa Keating, Cambridge

Department of Mathematics

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 extent 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.

auroux@math.berkeley.edu