Positively oriented ideal triangulations on hyperbolic three-manifolds |
| |
Authors: | Young-Eun Choi |
| |
Institution: | Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK |
| |
Abstract: | Let M3 be a non-compact hyperbolic 3-manifold that has a triangulation by positively oriented ideal tetrahedra. We show that the gluing variety defined by the gluing consistency equations is a smooth complex manifold with dimension equal to the number of boundary components of M3. Moreover, we show that the complex lengths of any collection of non-trivial boundary curves, one from each boundary component, give a local holomorphic parameterization of the gluing variety. As an application, some estimates for the size of hyperbolic Dehn surgery space of once-punctured torus bundles are given. |
| |
Keywords: | Hyperbolic three-manifold Positively oriented ideal triangulation Symplectic form Hyperbolic Dehn surgery space Punctured torus bundle |
本文献已被 ScienceDirect 等数据库收录! |
|