Book contents
- Frontmatter
- Contents
- Preface
- Drilling short geodesics in hyperbolic 3-manifolds
- On topologically tame Kleinian groups with bounded geometry
- An extension of the Masur domain
- Thurston's bending measure conjecture for once punctured torus groups
- Complexity of 3-manifolds
- Moduli of continuity of Cannon–Thurston maps
- Variations of McShane's identity for punctured surface groups
- Train tracks and the Gromov boundary of the complex of curves
- The pants complex has only one end
- The Weil–Petersson geometry of the five-times punctured sphere
- Convexity of geodesic-length functions: a reprise
- A proof of the Ahlfors finiteness theorem
- On the automorphic functions for Fuchsian groups of genus two
- Boundaries for two-parabolic Schottky groups
- Searching for the cusp
- Circle packings on surfaces with projective structures: a survey
- Grafting and components of quasi-fuchsian projective structures
- Computer experiments on the discreteness locus in projective structures
Preface
Published online by Cambridge University Press: 05 November 2011
- Frontmatter
- Contents
- Preface
- Drilling short geodesics in hyperbolic 3-manifolds
- On topologically tame Kleinian groups with bounded geometry
- An extension of the Masur domain
- Thurston's bending measure conjecture for once punctured torus groups
- Complexity of 3-manifolds
- Moduli of continuity of Cannon–Thurston maps
- Variations of McShane's identity for punctured surface groups
- Train tracks and the Gromov boundary of the complex of curves
- The pants complex has only one end
- The Weil–Petersson geometry of the five-times punctured sphere
- Convexity of geodesic-length functions: a reprise
- A proof of the Ahlfors finiteness theorem
- On the automorphic functions for Fuchsian groups of genus two
- Boundaries for two-parabolic Schottky groups
- Searching for the cusp
- Circle packings on surfaces with projective structures: a survey
- Grafting and components of quasi-fuchsian projective structures
- Computer experiments on the discreteness locus in projective structures
Summary
This volume is the proceedings of the programme Spaces of Kleinian Groups and Hyperbolic 3-Manifolds held at the Isaac Newton Institute in Cambridge, 21 July–15 August 2003. It is a companion volume to Kleinian Groups and Hyperbolic 3-Manifolds, London Mathematical Society Lecture Notes 299, the proceedings of a conference with the same title held at the Mathematics Institute, University of Warwick, 11–15 September 2001.
The period surrounding these two conferences has seen a series of remarkable advances in our understanding of hyperbolic structures on 3-manifolds. Many of the outstanding issues immediately preceding the Newton Institute meeting related to difficulties in extending results from manifolds with incompressible boundary to the general case. Proofs of Thurston's ending lamination conjecture and the Bers–Sullivan–Thurston density conjecture for general tame groups were announced at the meeting, and the picture was completed not long after the Newton programme, with two independent proofs of Marden's tameness conjecture. As a result, we now have a very clear understanding of the internal geometry of hyperbolic 3-manifolds, combined with an increasingly detailed, but quite intricate, picture of the topology and geometry of the associated deformation spaces of discrete groups.
The Newton Institute meeting turned out to be the international gathering at which many of these new results were disseminated. Almost all the primary contributors took part. Quite how rapid progress has been only became apparent to many of us during the meeting, which will be remembered as a milestone at which all of the new ideas were brought together.
- Type
- Chapter
- Information
- Spaces of Kleinian Groups , pp. vii - viiiPublisher: Cambridge University PressPrint publication year: 2006