Coxeter Decompositions of Hyperbolic Tetrahedra

Coxeter Decompositions of Bounded Hyperbolic Pyramids and Triangular Prisms

Coxeter decompositions of hyperbolic simplices where studied in math.MG/0212010 and math.MG/0210067. In this paper we use the methods of these works to classify Coxeter decompositions of bounded convex pyramids and triangular prisms in the hyperbolic space IH.

Coxeter decompositions of hyperbolic simplices

Commensurators of Cusped Hyperbolic Manifolds

This paper describes a general algorithm for finding the commensurator of a non-arithmetic hyperbolic manifold with cusps, and for deciding when two such manifolds are commensurable. The method is based on some elementary observations regarding horosphere packings and canonical cell decompositions. For example, we use this to find the commensurators of all non-arithmetic hyperbolic once-punctur...

The Volume Conjecture

6 Hyperbolic Geometry 31 6.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 6.2 Ideal Tetrahedra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 6.3 Volume of Ideal Hyperbolic Tetrahedra . . . . . . . . . . . . . . . . . . . . . . . . . . 37 6.4 Hyperbolic Manifolds . . . . . . . . . . . . . . . . . . . . . . . . ....

Non-peripheral Ideal Decompositions of Alternating Knots

An ideal triangulation T of a hyperbolic 3-manifold M with one cusp is non-peripheral if no edge of T is homotopic to a curve in the boundary torus of M . For such a triangulation, the gluing and completeness equations can be solved to recover the hyperbolic structure of M . A planar projection of a knot gives four ideal cell decompositions of its complement (minus 2 balls), two of which are id...