  Consider a Stein manifold M obtained by plumbing cotangent bundles of
manifolds of dimension greater than or equal to 3 at points. We prove that the
Fukaya category of closed exact Lagrangians with vanishing Maslov class in M is
generated by the compact cores of the plumbing. As applications, we classify
exact Lagrangian spheres in A2-Milnor fibres of arbitrary dimension, derive
constraints on exact Lagrangian fillings of Legendrian unknots in disk
cotangent bundles, and prove that the categorical equivalence given by the
spherical twist in a homology sphere is typically not realised by any compactly
supported symplectomorphism.

Symplectic Geometry