Positively oriented ideal triangulations on hyperbolic three-manifolds
By Young-Eun Choi. 2004
47 citations recorded by the source corpus.
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.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/9aee9a3597e887f25b195fb736023834672ec1d1
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- 6j–symbols, hyperbolic structures and the volume conjecture (2006, methodology): “ Tbe the triangulation of N\Lobtained by sub-triangulating each K-block in 8 tetrahedra. If ~a= ~1, it is sufficient to equip each block with the complete structure, otherwise by Choi’s Corollary 4.14 ([4]), we know that there exists Usuch that for each ~a∈ Uthere exists a unique set of geometric modu”
- An Introduction to Geometric Topology (2016, background): “13 has been proved by Choi [13] in 2004.”