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

Lee, Sangjin

doi:10.2140/agt.2024.24.655

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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

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Volume 24, issue 2 (2024)