Towards a higher-dimensional construction of stable/unstable Lagrangian laminations

Abstract

We generalize some properties of surface automorphisms of pseudo-Anosov type. First, we generalize the Penner construction of a pseudo-Anosov homeomorphism, and show that if a symplectic automorphism is constructed by our generalized Penner construction, then it has an invariant Lagrangian branched submanifold and an invariant Lagrangian lamination. These invariants are higher-dimensional generalizations of a train track and a geodesic lamination in the surface case. As an application, we compute the Lagrangian Floer homology of some Lagrangians on plumbings of cotangent bundles of spheres. © 2024 MSP (Mathematical Sciences Publishers).