Teichmüller theory via random simple closed curves
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912767860015104 |
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| author | McMullen, Curtis T. Torkaman, Tina |
| author_facet | McMullen, Curtis T. Torkaman, Tina |
| contents | We show the map $σ: T_g \to C_g$ sending a compact hyperbolic surface $X$ to a random simple closed geodesic on $X$ determines a proper embedding of Teichmüller space into the space of geodesic currents. The proof depends on a formula for the intersection number $i(C,C')$ of a pair of multicurves, expressed in terms of Dehn coordinates on $ML_g(\mathbb{Z})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_14101 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Teichmüller theory via random simple closed curves McMullen, Curtis T. Torkaman, Tina Geometric Topology Differential Geometry Dynamical Systems We show the map $σ: T_g \to C_g$ sending a compact hyperbolic surface $X$ to a random simple closed geodesic on $X$ determines a proper embedding of Teichmüller space into the space of geodesic currents. The proof depends on a formula for the intersection number $i(C,C')$ of a pair of multicurves, expressed in terms of Dehn coordinates on $ML_g(\mathbb{Z})$. |
| title | Teichmüller theory via random simple closed curves |
| topic | Geometric Topology Differential Geometry Dynamical Systems |
| url | https://arxiv.org/abs/2512.14101 |