Creating pseudo-Anosov Maps from Permutations and Matrices
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866914925823131648 |
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| author | Hubbard, John H. Rafiqi, Ahmad Schang, Tom |
| author_facet | Hubbard, John H. Rafiqi, Ahmad Schang, Tom |
| contents | We provide an integral combinatorial characterization of pseudo-Anosov maps on closed oriented surfaces of genus g > 1. We show that an orientation-preserving pseudo-Anosov homeomorphism with orientable foliations and fixing all critical trajectories can be encoded as a permutation of 2g+v-1 positive integers, where v is the number of singular points of the foliations (disregarding multiplicity). We call such a permutations an ordered block permutation (OBP), and it satisfies an admissiblity condition. Conversely, we show that a surface along with measured foliations (up to scaling) and the pseudo-Anosov map can be uniquely constructed out of the data of an admissible permutation of 2g+v-1 positive integers. In particular, for closed surfaces, we construct every orientable foliation invariant under a pseudo-Anosov homeomorphism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1902_07440 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Creating pseudo-Anosov Maps from Permutations and Matrices Hubbard, John H. Rafiqi, Ahmad Schang, Tom Dynamical Systems Algebraic Topology We provide an integral combinatorial characterization of pseudo-Anosov maps on closed oriented surfaces of genus g > 1. We show that an orientation-preserving pseudo-Anosov homeomorphism with orientable foliations and fixing all critical trajectories can be encoded as a permutation of 2g+v-1 positive integers, where v is the number of singular points of the foliations (disregarding multiplicity). We call such a permutations an ordered block permutation (OBP), and it satisfies an admissiblity condition. Conversely, we show that a surface along with measured foliations (up to scaling) and the pseudo-Anosov map can be uniquely constructed out of the data of an admissible permutation of 2g+v-1 positive integers. In particular, for closed surfaces, we construct every orientable foliation invariant under a pseudo-Anosov homeomorphism. |
| title | Creating pseudo-Anosov Maps from Permutations and Matrices |
| topic | Dynamical Systems Algebraic Topology |
| url | https://arxiv.org/abs/1902.07440 |