2017/11/27 by Keating, Ailsa
#FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.1711.09871
We are interested in comparing properties of symplectic mapping class groups of symplectic manifolds of dimension four or higher with properties of classical mapping class groups of surfaces. For n ≥ 2, consider a configuration of Lagrangian Sns in a Weinstein domain M2n. If it is analogous, in some sense that we make precise, to a configuration of exact Lagrangian S1s on a surface Σ, we show that any relation between Dehn twists in the Sns must also hold between the S1s. Such analogous pairs of configurations include plumbings of T^∗ S1s and T^∗ Sns with the same plumbing graph, and vanishing cycles for a two-variable singularity and for its stabilisation. We give a number of corollaries for subgroups of symplectic mapping class groups.