Thurston construction mapping classes with minimal dilatation
| Autor: | Contractor, Maryam, Reed, Otto |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | Given a pair of filling curves $\alpha, \beta$ on a surface of genus $g$ with $n$ punctures, we explicitly compute the mapping classes realizing the minimal dilatation over all the pseudo-Anosov maps given by the Thurston construction on $\alpha,\beta$. We do so by solving for the minimal spectral radius in a congruence subgroup of $\text{PSL}_2(\mathbb{Z})$. We apply this result to realized lower bounds on intersection number between $\alpha$ and $\beta$ to give the minimal dilatation over any Thurston construction pA map on $\Sigma_{g,n}$ given by a filling pair $\alpha \cup \beta$. Comment: 11 pages, 3 figures |
| Databáze: | arXiv |
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