Continuity of the bending map
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2004
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866912644772921344 |
|---|---|
| author | Lecuire, Cyril |
| author_facet | Lecuire, Cyril |
| contents | The bending map of a hyperbolic 3-manifold maps a convex cocompact hyperbolic metric on a hyperbolic 3-manifold with boundary to its bending measured geodesic lamination. In the present paper we study the extension of this map to the space of geometrically finite hyperbolic metrics. We introduce a relationship on the space of measured geodesic laminations and shows that the quotient map obtained from the bending map is continuous. October 2025, an erratum has been added that corrects an error in the main Theorem. The topology used in the quotient space should not be the quotient topology but the "tubular topology" defined in this erratum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0411412 |
| institution | arXiv |
| publishDate | 2004 |
| record_format | arxiv |
| spellingShingle | Continuity of the bending map Lecuire, Cyril Differential Geometry 30F40, 20H10 The bending map of a hyperbolic 3-manifold maps a convex cocompact hyperbolic metric on a hyperbolic 3-manifold with boundary to its bending measured geodesic lamination. In the present paper we study the extension of this map to the space of geometrically finite hyperbolic metrics. We introduce a relationship on the space of measured geodesic laminations and shows that the quotient map obtained from the bending map is continuous. October 2025, an erratum has been added that corrects an error in the main Theorem. The topology used in the quotient space should not be the quotient topology but the "tubular topology" defined in this erratum. |
| title | Continuity of the bending map |
| topic | Differential Geometry 30F40, 20H10 |
| url | https://arxiv.org/abs/math/0411412 |