Thurston construction mapping classes with minimal dilatation
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866929643764842496 |
|---|---|
| author | Contractor, Maryam Reed, Otto |
| author_facet | Contractor, Maryam Reed, Otto |
| contents | Given a pair of filling curves $α, β$ 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 $α,β$. 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 $α$ and $β$ to give the minimal dilatation over any Thurston construction pA map on $Σ_{g,n}$ given by a filling pair $α\cup β$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16314 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Thurston construction mapping classes with minimal dilatation Contractor, Maryam Reed, Otto Geometric Topology General Topology Given a pair of filling curves $α, β$ 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 $α,β$. 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 $α$ and $β$ to give the minimal dilatation over any Thurston construction pA map on $Σ_{g,n}$ given by a filling pair $α\cup β$. |
| title | Thurston construction mapping classes with minimal dilatation |
| topic | Geometric Topology General Topology |
| url | https://arxiv.org/abs/2412.16314 |