Standardly embedded train tracks and pseudo-Anosov maps with minimum expansion factor
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866929196942491648 |
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| author | Hironaka, Eriko Tsang, Chi Cheuk |
| author_facet | Hironaka, Eriko Tsang, Chi Cheuk |
| contents | We show that given a fully-punctured pseudo-Anosov map $f:S \to S$ whose punctures lie in at least two orbits under the action of $f$, the expansion factor $λ(f)$ satisfies the inequality $λ(f)^{|χ(S)|} \ge μ^4 \approx 6.85408$, where $μ= \frac{1 + \sqrt{5}}{2} \approx 1.61803$ is the golden ratio. The proof involves a study of standardly embedded train tracks, and the Thurston symplectic form defined on their weight space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_13418 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Standardly embedded train tracks and pseudo-Anosov maps with minimum expansion factor Hironaka, Eriko Tsang, Chi Cheuk Geometric Topology Dynamical Systems We show that given a fully-punctured pseudo-Anosov map $f:S \to S$ whose punctures lie in at least two orbits under the action of $f$, the expansion factor $λ(f)$ satisfies the inequality $λ(f)^{|χ(S)|} \ge μ^4 \approx 6.85408$, where $μ= \frac{1 + \sqrt{5}}{2} \approx 1.61803$ is the golden ratio. The proof involves a study of standardly embedded train tracks, and the Thurston symplectic form defined on their weight space. |
| title | Standardly embedded train tracks and pseudo-Anosov maps with minimum expansion factor |
| topic | Geometric Topology Dynamical Systems |
| url | https://arxiv.org/abs/2210.13418 |