Coordinates for Quasi-Fuchsian Punctured Torus Space

Linear Slices of the Quasi-fuchsian Space of Punctured Tori

After fixing a marking (V,W ) of a quasi-Fuchsian punctured torus group G, the complex length λV and the complex twist τV,W parameters define a holomorphic embedding of the quasi-Fuchsian space QF of punctured tori into C2. It is called the complex Fenchel-Nielsen coordinates of QF . For c ∈ C, let Qγ,c be the affine subspace of C2 defined by the linear equation λV = c. Then we can consider the...

Spirals in the Boundary of Slices of Quasi-fuchsian Space

We prove that the Bers and Maskit slices of the quasi-Fuchsian space of a once-punctured torus have a dense, uncountable set of points in their boundaries about which the boundary spirals infinitely.

The Classification of Punctured-torus Groups

Thurston’s ending lamination conjecture proposes that a finitelygenerated Kleinian group is uniquely determined (up to isometry) by the topology of its quotient and a list of invariants that describe the asymptotic geometry of its ends. We present a proof of this conjecture for punctured-torus groups. These are free two-generator Kleinian groups with parabolic commutator, which should be though...

On Hyperbolic Polyhedra Arising as Convex Cores of Quasi-Fuchsian Punctured Torus Groups

Pleating invariants for punctured torus groups

In this paper we give a complete description of the space QF of quasifuchsian punctured torus groups in terms of what we call pleating invariants. These are natural invariants of the boundary ∂C of the convex core of the associated hyperbolic 3-manifold M and give coordinates for the non-Fuchsian groups QF −F . The pleating invariants of a component of ∂C consist of the projective class of its ...