Trace field degrees in the Torelli group
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912758610526208 |
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| author | Lanneau, Erwan Liechti, Livio |
| author_facet | Lanneau, Erwan Liechti, Livio |
| contents | We show that for $g\ge 2$, all integers $1 \le d \le 3g-3$ arise as trace field degrees of pseudo-Anosov mapping classes in the Torelli group of the closed orientable surface of genus $g$. Our method uses the Thurston-Veech construction of pseudo-Anosov maps, and we provide examples where the stretch factor has algebraic degree any even number between two and $6g-6$. This validates a claim by Thurston from the 1980s. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_17194 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Trace field degrees in the Torelli group Lanneau, Erwan Liechti, Livio Geometric Topology Dynamical Systems 57K20, 11R09 We show that for $g\ge 2$, all integers $1 \le d \le 3g-3$ arise as trace field degrees of pseudo-Anosov mapping classes in the Torelli group of the closed orientable surface of genus $g$. Our method uses the Thurston-Veech construction of pseudo-Anosov maps, and we provide examples where the stretch factor has algebraic degree any even number between two and $6g-6$. This validates a claim by Thurston from the 1980s. |
| title | Trace field degrees in the Torelli group |
| topic | Geometric Topology Dynamical Systems 57K20, 11R09 |
| url | https://arxiv.org/abs/2405.17194 |