Related papers: Angle structures and hyperbolic $3$-manifolds with…

We consider hyperbolic manifolds with boundary, which admit an ideal triangulation with n ideal triangles and one edge. We prove that the number of these manifolds is $\exp(n\ln(n)+O(n))$.

L. Paoluzzi constructed a family of compact orientable three-dimensional hyperbolic manifolds with totally geodesic boundary, which were, by construction, closely related to the three-dimensional torus. This paper gives their complete…

In proper hyperbolic geodetic spaces we construct rooted $\mathbb R$-trees with the following properties. On the one hand, every ray starting at the root is quasi-geodetic; so these $\mathbb R$-trees represent the space itself well. At the…

For a given cusped 3-manifold $M$ admitting an ideal triangulation, we describe a method to rigorously prove that either $M$ or a filling of $M$ admits a complete hyperbolic structure via verified computer calculations. Central to our…

In this paper, we find infinite hyperbolic 3-manifolds that admit no weakly symplectically fillable contact structures, using tools in Heegaard Floer theory. We also remark that part of these manifolds do admit tight contact structures.

A 4-manifold is constructed with some curious metric properties; or maybe it is many 4-manifolds masquerading as one, which would explain why it looks curious. Anyway, knots in the 3-sphere with complete finite volume hyperbolic metrics on…

We show there is an upper bound on the diameter of a closed, hyperbolic 3-manifold in terms of the length of any presentation of its fundamental group.

Let M be the interior of a compact 3-manifold with non-empty boundary, and T be an ideal (topological) triangulation of M. This paper describes necessary and sufficient conditions for the existence of angle structures, semi-angle structures…

The Heegaard genus of a 3-manifold, as well as the growth of Heegaard genus in its finite sheeted cover spaces, has extensively been studied in terms of algebraic, geometric and topological properties of the 3-manifold. This note shows that…

In this paper we present a necessary conditions, that simple close geodesics on regular tetrahedra in the 3-dimensional hyperbolic space must satisfy. Furthermore, we explicitly describe three classes of simple closed geodesics on regular…

This is the second in a series of papers in which we investigate ideal triangulations of the interiors of compact 3-manifolds with tori or Klein bottle boundaries. Such triangulations have been used with great effect, following the…

We show that the hyperbolic structure on a closed, orientable, hyperbolic 3-manifold can be constructed from a solution to the hyperbolic gluing equations using any triangulation with essential edges. The key ingredients in the proof are…

A taut foliation of a hyperbolic 3-manifold has the continuous extension property for leaves in almost every direction; that is, for each leaf of the universal cover of the foliation and almost every geodesic ray in the leaf, the limit of…

Let $S$ be an oriented closed surface of genus at least two, and let $M = S \times (0,1)$. Suppose that $h$ is a Riemannian metric on $S$ with curvature strictly greater than $-1$, $h^{*}$ is a Riemannian metric on $S$ with curvature…

We extend the complete census of orientable cusped hyperbolic $3$-manifolds to $10$ tetrahedra, giving the next $150730$ manifolds and their $496638$ minimal ideal triangulations. As applications, we find the precisely $439898$ exceptional…

Given any connected, open 3-manifold $U$ having finitely many ends, a non-compact 3-manifold $M$ is constructed having the following properties: the interior of $M$ is homeomorphic to $U$; the boundary of $M$ is the disjoint union of…

Myers shows that every compact, connected, orientable $3$--manifold with no $2$--sphere boundary components contains a hyperbolic knot. We use work of Ikeda with an observation of Adams-Reid to show that every $3$--manifold subject to the…

We construct a K\"ahler structure (${\mathbb{J}},\Omega,{\mathbb{G}}$) on the space ${\mathbb{L}}({\mathbb{H}}^3)$ of oriented geodesics of hyperbolic 3-space ${\mathbb{H}}^3$ and investigate its properties. We prove that…

We show that some hyperbolic 3-manifolds which are tessellated by copies of the regular ideal hyperbolic tetrahedron embed geodesically in a complete, finite volume, hyperbolic 4-manifold. This allows us to prove that the complement of the…

Agol recently introduced the notion of a veering triangulation, and showed that such triangulations naturally arise as layered triangulations of fibered hyperbolic 3-manifolds. We prove, by a constructive argument, that every veering…