Agol cycles of pseudo-Anosov maps on the 2-punctured torus and 5-punctured sphere
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910619146387456 |
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| author | Bellynck, Jean-Baptiste Kin, Eiko |
| author_facet | Bellynck, Jean-Baptiste Kin, Eiko |
| contents | Given a periodic splitting sequence of a measured train track, an Agol cycle is the part that constitutes a period up to the action of a pseudo-Anosov map and the rescaling by its dilatation. We consider a family of pseudo-Anosov maps on the 2-punctured torus and on the 5-punctured sphere. We present measured train tracks and compute their Agol cycles. We give a condition under which two maps in the defined family are conjugate or not. In the process, we find a new formula for the dilatation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_16423 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Agol cycles of pseudo-Anosov maps on the 2-punctured torus and 5-punctured sphere Bellynck, Jean-Baptiste Kin, Eiko Geometric Topology 57M50 (Primary) 20F36, 57M60 (Secondary) Given a periodic splitting sequence of a measured train track, an Agol cycle is the part that constitutes a period up to the action of a pseudo-Anosov map and the rescaling by its dilatation. We consider a family of pseudo-Anosov maps on the 2-punctured torus and on the 5-punctured sphere. We present measured train tracks and compute their Agol cycles. We give a condition under which two maps in the defined family are conjugate or not. In the process, we find a new formula for the dilatation. |
| title | Agol cycles of pseudo-Anosov maps on the 2-punctured torus and 5-punctured sphere |
| topic | Geometric Topology 57M50 (Primary) 20F36, 57M60 (Secondary) |
| url | https://arxiv.org/abs/2409.16423 |