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

Sangjin Lee
Algebraic & Geometric Topology 24 (2024) 655–716
DOI: 10.2140/agt.2024.24.655
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.

Keywords
Lagrangian lamination, pseudo-Anosov, symplectic automorphism
Mathematical Subject Classification 2010
Primary: 53D05, 53D40, 57R17
References
Publication
Received: 13 August 2019
Revised: 26 July 2022
Accepted: 9 August 2022
Published: 12 April 2024
Authors
Sangjin Lee
Center for Geometry and Physics
Institute for Basic Science
Pohang
South Korea
https://sites.google.com/view/sangjinlee/home
© 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY).

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