Towards a higher-dimensional construction of stable/unstable Lagrangian laminations
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arXiv
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| Format: | Preprint |
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2019
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| _version_ | 1866916218805420032 |
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| author | Lee, Sangjin |
| author_facet | Lee, Sangjin |
| contents | 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 $ψ$ and a Lagrangian branched surface $B_ψ$ satisfies some assumptions, we prove that there is an invariant Lagrangian lamination $\mathcal{L}$ which is a higher-dimensional generalization of a geodesic lamination. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1903_09472 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Towards a higher-dimensional construction of stable/unstable Lagrangian laminations Lee, Sangjin Symplectic Geometry 57R17, 57R30, 53D05 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 $ψ$ and a Lagrangian branched surface $B_ψ$ satisfies some assumptions, we prove that there is an invariant Lagrangian lamination $\mathcal{L}$ which is a higher-dimensional generalization of a geodesic lamination. |
| title | Towards a higher-dimensional construction of stable/unstable Lagrangian laminations |
| topic | Symplectic Geometry 57R17, 57R30, 53D05 |
| url | https://arxiv.org/abs/1903.09472 |