Exact Lagrangians in plumbings

Abstract

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.

39 pages, 5 figures. Versions 2,3: minor corrections and clarifications

References in corpus (2)

• Effect of Legendrian Surgery
• Nearby Lagrangians with vanishing Maslov class are homotopy equivalent

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