Related papers: Cone-manifolds and the density conjecture

We study spaces obtained from a complete finite volume complex hyperbolic n-manifold M by removing a compact totally geodesic complex (n-1)-submanifold. The main result is that the fundamental group of M-S is relatively hyperbolic, relative…

We prove a structure theorem for 3-manifolds with non-trivial JSJ-decomposition and 2-generated fundamental group. We deduce a variety of Corollaries. Note this is not a complete classification of such manifolds. In particular we believe…

We consider a compact orientable hyperbolic 3-manifold with a compressible boundary. Suppose that we are given a sequence of geometrically finite hyperbolic metrics whose conformal boundary structures at infinity diverge to a projective…

We prove that every complete finite-volume hyperbolic 3-manifold $M$ that is tessellated into (embedded) right-angled regular polyhedra (dodecahedra or ideal octahedra) embeds geodesically in a complete finite-volume connected orientable…

This paper contains examples of closed aspherical manifolds obtained as a by-product of recent work by the author [arXiv:math.GR/0509490] on the relative strict hyperbolization of polyhedra. The following is proved. (I) Any closed…

Following on from work of Dunfield, we determine the fibred status of all the unknown hyperbolic 3-manifolds in the cusped census. We then find all the fibred hyperbolic 3-manifolds in the closed census and use this to find over 100…

This is the third in a series of papers constructing hyperbolic structures on all Haken three-manifolds. This portion deals with the mixed case of the deformation space for manifolds with incompressible boundary that are not acylindrical,…

D. D. Long and A. W. Reid have shown that some compact flat 3-manifold cannot be diffeomorphic to a cusp cross-section of any complete finite volume 1-cusped real hyperbolic 4-manifold. This note concerns the complex hyperbolic case. We…

A version of a conjecture of McMullen is as follows: Given a hyperbolizable 3-manifold M with incompressible boundary, there exists a uniform constant K such that if N is a hyperbolic 3-manifold homeomorphic to the interior of M, then the…

We show that a 3-manifold containing an incompressible surface has topologically minimal surfaces of arbitrary high genus.

We show that every sequence of torsion-free arithmetic congruence lattices in $\mathrm{PGL}(2,\mathbb R)$ or $\mathrm{PGL}(2,\mathbb C)$ satisfies a strong quantitative version of the Limit Multiplicity property. We deduce that for $R>0$ in…

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…

We explore the limit set of a particular spherical CR uniformization of a cusped hyperbolic manifold. We prove that the limit set is the closure of a countable union of $\mathbb{R}$-circles, is connected, and contains a Hopf link with three…

In this paper, we prove that profinitely rigid finite-volume hyperbolic manifolds form a closed set under geometric topology. This observation implies the profinite rigidity of a large family of cusped hyperbolic manifolds via…

We give an upper bound for the number of compact essential orientable non-isotopic surfaces, with Euler characteristic at least some constant $\chi$, properly embedded in a finite-volume hyperbolic 3-manifold $M$, closed or cusped. This…

We classify all the non-hyperbolic Dehn fillings of the complement of the chain-link with 3 components, conjectured to be the smallest hyperbolic 3-manifold with 3 cusps. We deduce the classification of all non-hyperbolic Dehn fillings of…

We prove hyperbolic 3-manifolds are geometrically inflexible: a unit quasiconformal deformation of a Kleinian group extends to an equivariant bi-Lipschitz diffeomorphism between quotients whose pointwise bi-Lipschitz constant decays…

We count the number of conjugacy classes of maximal, genus g, surface subroups in hyperbolic 3-manifold groups. For any closed hyperbolic 3-manifold, we show that there is an upper bound on this number which grows factorially with g. We…

We prove that every finitely generated group with recursive aspherical presentation embeds into a group with finite aspherical presentation. This and several known facts about groups and manifolds imply that there exists a 4-dimensional…

We show the 3-manifold at infinity of the complex hyperbolic triangle group $\Delta_{3,\infty,\infty;\infty}$ is the three-cusped "magic" 3-manifold $6_1^3$. We also show the 3-manifold at infinity of the complex hyperbolic triangle group…