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

Towards a higher-dimensional construction of stable/unstable Lagrangian laminations SANGJIN LEEWe 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.53D05, 53D40, 57R17