Marden conjectured that a hyperbolic 3-manifold M with finitely generated fundamental group is tame, i.e. it is homeomorphic to the interior of a compact manifold with boundary [42]. Since then, manyâ€¦ (More)

In this paper, we find lower bounds for the volumes of certain hyperbolic Haken 3manifolds. The theory of Jorgensen and Thurston shows that the volumes of hyperbolic 3-manifolds are well-ordered, butâ€¦ (More)

We prove that cubulated hyperbolic groups are virtually special. The proof relies on results of Haglund and Wise which also imply that they are linear groups, and quasi-convex subgroups areâ€¦ (More)

We show that for a hyperbolic knot complement, all but at most 12 Dehn fillings are irreducible with infinite word-hyperbolic fundamental group. AMS Classification numbers Primary: 57M50, 57M27â€¦ (More)

We prove that an irreducible 3-manifold whose fundamental group satisfies a certain group-theoretic property called RFRS is virtually fibered. As a corollary, we show that 3-dimensional reflectionâ€¦ (More)

We show that 3-MANIFOLD KNOT GENUS, the problem of deciding whether a polygonal knot in a closed three-dimensional manifold bounds a surface of genus at most g, is NP-complete. We also show that theâ€¦ (More)

We prove that there are only finitely many arithmetic Kleinian maximal reflection groups. Mathematics Subject Classification (2000). Primary 30F40; Secondary 57M.

We show that there are algorithms to determine if a 3-manifold contains an essential lamination or a Reebless foliation. AMS Classification numbers Primary: 57M50

Given a hyperbolic 3{manifold M containing an embedded closed geodesic, we estimate the volume of a complete hyperbolic metric on the complement of the geodesic in terms of the geometry of M . As aâ€¦ (More)

One of the central questions in topology is determining whether a given curve is knotted or unknotted. An algorithm to decide this question was given by Haken in 1961, using the technique of normalâ€¦ (More)