Towards a higher dimensional construction of stable/unstable Lagrangian laminations
- Author(s): Lee, Sangjin
- Advisor(s): Honda, Ko
- et al.
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 a symplectic automorphism which is constructed by our generalized
Penner construction has an invariant Lagrangian branched submanifold and an invariant
Lagrangian lamination, which are higher-dimensional generalizations of a
train track and a geodesic lamination in the surface case. Moreover, if a pair consisting
of a symplectic automorphism and a Lagrangian branched surface B satisfies
some assumptions, we prove that there is an invariant Lagrangian lamination L
which is a higher-dimensional generalization of a geodesic lamination.