On symplectic stabilisations and mapping classes

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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 $n \geqslant 2$ , consider a configuration of Lagrangian S n $S^n$ s in a Weinstein domain M 2 n $M^{2n}$ . If it is analogous, in some sense that we make precise, to a configuration of exact Lagrangian S 1 $S^1$ s on a surface Σ $\Sigma$ , we show that any relation between Dehn twists in the S n $S^n$ s must also hold between the S 1 $S^1$ s. Such analogous pairs of configurations include plumbings of T * S 1 $T^\ast S^1$ s and T * S n $T^\ast S^n$ s 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.