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Towards a higher-dimensional construction of stable/unstable Lagrangian laminations
- Source :
- Algebr. Geom. Topol. 24 (2024) 655-716
- Publication Year :
- 2019
-
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 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 $\psi$ and a Lagrangian branched surface $B_{\psi}$ satisfies some assumptions, we prove that there is an invariant Lagrangian lamination $\mathcal{L}$ which is a higher-dimensional generalization of a geodesic lamination.<br />Comment: 43 pages, 10 figures
- Subjects :
- Mathematics - Symplectic Geometry
57R17, 57R30, 53D05
Subjects
Details
- Database :
- arXiv
- Journal :
- Algebr. Geom. Topol. 24 (2024) 655-716
- Publication Type :
- Report
- Accession number :
- edsarx.1903.09472
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.2140/agt.2024.24.655