Construction and recognition of hyperbolic 3-manifolds with geodesic boundary
By Roberto Frigerio, Carlo Petronio. 2001
47 citations recorded by the source corpus.
We extend to the context of hyperbolic 3-manifolds with geodesic boundary Thurston's approach to hyperbolization by means of geometric triangulations. In particular, we introduce moduli for (partially) truncated hyperbolic tetrahedra, and we discuss consistency and completeness equations. Moreover, building on previous work of Ushijima, we extend Weeks' tilt formula algorithm, which computes the Epstein-Penner canonical decomposition, to an algorithm that computes the Kojima decomposition. Our theory has been exploited to classify all the orientable finite-volume hyperbolic 3-manifolds with non-empty compact geodesic boundary admitting an ideal triangulation with at most four tetrahedra. The theory is particularly interesting in the case of complete finite-volume manifolds with geodesic boundary in which the boundary is non-compact. We include this case using a suitable adjustment of the notion of ideal triangulation, and we show how this case arises within the theory of knots and links.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/7cde2dc20de757085d061856df616852563bdc24
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
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, background): “s proper then the sum of the three dihedral angles (computed through the hyperbolic metric on H3) around each vertex is greater than πand, if it is hyperideal then it is less than π(see Theorem 2.2 of[9] for a proof of this statement). Let now T(~θ) be a tetrahedron whose dihedral angles are given b”
- A combinatorial curvature flow for compact 3-manifolds with boundary (2004, methodology): “In the 3-dimensional case, the basic building blocks are the strictly hyperideal tetrahedra discovered by Bao and Bonahon [BB]. See also Frigerio and Petronio [ FP ].”