Simple length spectra as moduli for hyperbolic surfaces and rigidity of length identities
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2020
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913896614330368 |
|---|---|
| author | Baik, Hyungryul Choi, Inhyeok Kim, Dongryul M. |
| author_facet | Baik, Hyungryul Choi, Inhyeok Kim, Dongryul M. |
| contents | In this article, we revisit classical length identities enjoyed by simple closed curves on hyperbolic surfaces. We state and prove the rigidity of such identities over Teichmüller spaces. Due to this rigidity, certain collections of simple closed curves which minimally intersect are characterized on generic hyperbolic surfaces by their lengths.
As an application, we construct a meagre set $V$ in the Teichmüller space of a topological orientable surface $S$, possibly of infinite type. Then the isometry class of a (Nielsen-convex) hyperbolic structure on $S$ outside $V$ is characterized by its unmarked simple length spectrum. Namely, we show that the simple length spectra can be used as moduli for generic hyperbolic surfaces. In the case of compact surfaces, an analogous result using length spectra was obtained by Wolpert. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_05652 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Simple length spectra as moduli for hyperbolic surfaces and rigidity of length identities Baik, Hyungryul Choi, Inhyeok Kim, Dongryul M. Geometric Topology Differential Geometry 30F60, 57M50, 32G15 In this article, we revisit classical length identities enjoyed by simple closed curves on hyperbolic surfaces. We state and prove the rigidity of such identities over Teichmüller spaces. Due to this rigidity, certain collections of simple closed curves which minimally intersect are characterized on generic hyperbolic surfaces by their lengths. As an application, we construct a meagre set $V$ in the Teichmüller space of a topological orientable surface $S$, possibly of infinite type. Then the isometry class of a (Nielsen-convex) hyperbolic structure on $S$ outside $V$ is characterized by its unmarked simple length spectrum. Namely, we show that the simple length spectra can be used as moduli for generic hyperbolic surfaces. In the case of compact surfaces, an analogous result using length spectra was obtained by Wolpert. |
| title | Simple length spectra as moduli for hyperbolic surfaces and rigidity of length identities |
| topic | Geometric Topology Differential Geometry 30F60, 57M50, 32G15 |
| url | https://arxiv.org/abs/2012.05652 |