Sur la composition des formes quadratiques quaternaires et ses applications aux groupes fuchsiens
Surgeries on small volume hyperbolic 3-orbifolds.
Tameness on the boundary and Ahlfors' measure conjecture
Let N be a complete hyperbolic 3-manifold that is an algebraic limit of geometrically finite hyperbolic 3-manifolds. We show N is homeomorphic to the interior of a compact 3-manifold, or tame, if one of the following conditions holds: 1. N has non-empty conformal boundary, 2. N is not homotopy equivalent to a compression body, or 3. N is a strong limit of geometrically finite manifolds. The first case proves Ahlfors’ measure conjecture for kleinian groups in the closure of the geometrically finite...
The bounded model for hyperbolic 3-space and a quaternionic uniformization theorem.
The box-counting dimension for geometrically finite Kleinian groups
We calculate the box-counting dimension of the limit set of a general geometrically finite Kleinian group. Using the 'global measure formula' for the Patterson measure and using an estimate on the horoball counting function we show that the Hausdorff dimension of the limit set is equal to both: the box-counting dimension and packing dimension of the limit set. Thus, by a result of Sullivan, we conclude that for a geometrically finite group these three different types of dimension coincide with the...
The chordal norm of discrete Möbius groups in several dimensions.
The classification of punctured-torus groups.
The density at infinity of a discrete group of hyperbolic motions
The equivariant fundamental group, uniformization of real algebraic curves, and global complex analytic coordinates on Teichmüller spaces
The finite subgroups of maximal arithmetic kleinian groups
Given a maximal arithmetic Kleinian group , we compute its finite subgroups in terms of the arithmetic data associated to by Borel. This has applications to the study of arithmetic hyperbolic 3-manifolds.
The interior of discrete projective structures in the Bers fiber.
The limit map of a homomorphism of discrete Möbius groups
The mixed elliptically fixed point property for Kleinian groups.
The monodromy groups of Schwarzian equations on closed Riemann surfaces.
The multiplier-series of a Schottky group.
The outside of the Teichmüller space of punctured tori in Maskit's embedding.
The topology of deformation spaces of Kleinian groups.
Topologie de Gromov équivariante, structures hyperboliques et arbres réels.
Traces, lengths, axes and commensurability
The focus of this paper are questions related to how various geometric and analytical properties of hyperbolic 3-manifolds determine the commensurability class of such manifolds. The paper is for the large part a survey of recent work.
Traces of commutators of Möbius transformations.