Related papers: Hyperbolic 3-manifolds with large kissing number

The maximum possible number of non-overlapping unit spheres that can touch a unit sphere in $n$ dimensions is called kissing number. The problem for finding kissing numbers is closely connected to the more general problems of finding bounds…

Periodic geodesics on the modular surface correspond to periodic orbits of the geodesic flow in its unit tangent bundle $\mathrm{PSL}_2(\mathbb{Z})\backslash\mathrm{PSL}_2(\mathbb{R})$. The complement of any finite number of orbits is a…

Let $M$ be a 1-cusped hyperbolic 3-manifold. In this paper, we study the behavior of $N_M(v)$, the number of Dehn fillings of $M$ with a given volume $v(\in \mathbb{R})$. We conduct extensive computational experiments to estimate $N_M$ and…

We consider non-orientable hyperbolic 3-manifolds of finite volume $M^3$. When $M^3$ has an ideal triangulation $\Delta$, we compute the deformation space of the pair $(M^3, \Delta)$ (its Neumann Zagier parameter space). We also determine…

This paper provides upper and lower bounds on the kissing number of congruent radius $r > 0$ spheres in $\mathbb{H}^n$, for $n\geq 2$. For that purpose, the kissing number is replaced by the kissing function $\kappa(n, r)$ which depends on…

Recently A. Schrijver derived new upper bounds for binary codes using semidefinite programming. In this paper we adapt this approach to codes on the unit sphere and we compute new upper bounds for the kissing number in several dimensions.…

We prove that the space $\mathcal{H}_\infty$ of framed infinite volume hyperbolic $3$-manifolds is connected but not path connected. Two proofs of connectivity of this space, which is equipped with the geometric topology, are given, each…

The main thrust of present note is a volume formula for hyperbolic surface bundle with the fundamental group G. The novelty consists in a purely algebraic approach to the above problem. Initially, we concentrate on the Baum-Connes morphism…

In this article we study the spectrum of totally geodesic surfaces of a finite volume hyperbolic 3-manifold. We show that for arithmetic hyperbolic 3-manifolds that contain a totally geodesic surface, this spectrum determines the…

We give examples of closed hyperbolic 3-manifolds with first Betti number 2 and 3 for which no sequence of finite abelian covering spaces increases the first Betti number. For 3-manifolds $M$ with first Betti number 2 we give a…

Given a closed hyperbolic 3-manifold $M$, we construct a tower of covers with increasing Heegaard genus, and give an explicit lower bound on the Heegaard genus of such covers as a function of their degree. Using similar methods we prove…

Let ${\mathfrak M}$ be a closed, orientable, hyperbolic 3-orbifold whose singular set is a link, and such that $\pi_1({\mathfrak M})$ contains no hyperbolic triangle group. We show that if the underlying manifold $|{\mathfrak M}|$ is…

In this paper we show that the volume of a maximal globally hyperbolic Cauchy-compact anti-de Sitter $3$-manifold $M$ is at least $\pi^2|\chi(M)|$, and that this minimum value is attained if and only if $M$ is Fuchsian.

If M is a closed simple 3-manifold whose fundamental group contains a genus-g surface group for some g>1, and if the dimension of H_1(M;Z_2) is at least max(3g-1,6), we show that M contains a closed, incompressible surface of genus at most…

Given the fundamental group $\Gamma$ of a finite-volume complete hyperbolic $3$-manifold $M$, it is possible to associate to any representation $\rho:\Gamma \rightarrow \text{Isom}(\mathbb{H}^3)$ a numerical invariant called volume. This…

We describe a natural strategy to enumerate compact hyperbolic 3-manifolds with geodesic boundary in increasing order of complexity. We show that the same strategy can be employed to analyze simultaneously compact manifolds and…

We show if M is a closed, connected, orientable, hyperbolic 3-manifold with Heegaard genus g then g >= 1/2 cosh(r) where r denotes the radius of any isometrically embedded ball in M. Assuming an unpublished result of Pitts and Rubinstein…

We show that there is an upper bound on the injectivity radius of a hyperbolic 3-manifold in terms of the the number of generators of its fundamental group.

We investigate the conjectural relations between the Reshetikhin-Turaev-Witten quantum SU(2) invariants and the volume of hyperbolic 3-manifolds. Given a finite set of sufficiently large positive integers, say J, we construct examples of…

We construct hyperbolic integer homology 3-spheres where the injectivity radius is arbitrarily large for nearly all points of the manifold. As a consequence, there exists a sequence of closed hyperbolic 3-manifolds which Benjamini-Schramm…