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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
Lee, Sangjin 1
@article{10_2140_agt_2024_24_655,
author = {Lee, Sangjin},
title = {Towards a higher-dimensional construction of stable/unstable {Lagrangian} laminations},
journal = {Algebraic and Geometric Topology},
pages = {655--716},
publisher = {mathdoc},
volume = {24},
number = {2},
year = {2024},
doi = {10.2140/agt.2024.24.655},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.655/}
}
TY - JOUR AU - Lee, Sangjin TI - Towards a higher-dimensional construction of stable/unstable Lagrangian laminations JO - Algebraic and Geometric Topology PY - 2024 SP - 655 EP - 716 VL - 24 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.655/ DO - 10.2140/agt.2024.24.655 ID - 10_2140_agt_2024_24_655 ER -
%0 Journal Article %A Lee, Sangjin %T Towards a higher-dimensional construction of stable/unstable Lagrangian laminations %J Algebraic and Geometric Topology %D 2024 %P 655-716 %V 24 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.655/ %R 10.2140/agt.2024.24.655 %F 10_2140_agt_2024_24_655
Lee, Sangjin. Towards a higher-dimensional construction of stable/unstable Lagrangian laminations. Algebraic and Geometric Topology, Tome 24 (2024) no. 2, pp. 655-716. doi: 10.2140/agt.2024.24.655
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