Kleinian Groups and Hyperbolic 3-Manifolds

The subject of Kleinian groups and hyperbolic 3-manifolds is currently undergoing explosively fast development, with many old problems and conjectures close to resolution. This volume, proceedings of the Warwick workshop in September 2001, contains expositions of many of these breakthroughs including Minskys lectures on the first half of the proof of the Ending Lamination Conjecture, the Bers Density Conjecture by Brock and Bromberg, the Tameness Conjecture by Kleineidam and Souto, the state of the art in cone manifolds by Hodgson and Kerckhoff, and the counter example to Thurston’s K=2 conjecture by Epstein, Marden and Markovic. It also contains Jørgensens famous paper ‘On pairs of once punctured tori’ in print for the first time. The excellent collection of papers here will appeal to graduate students, who will find much here to inspire them, and established researchers who will find this valuable as a snapshot of current research.

Spis treści:
Part I. Hyperbolic 3-Manifolds
1. Combinatorial and geometrical aspects of hyperbolic 3-manifolds Y. Minsky
2. Harmonic deformations of hyperbolic 3-manifolds C. D. Hodgson and S. P. Kerchoff
3. Cone-manifolds and the density conjecture J. F. Brock and K. W. Bromberg
4. Les géodésiques fermés dune variété hyperbolique en tant que noeuds J.-P. Otal
5. Ending laminations in the Masur domain G. Kleineidam and J. Souto
6. Quasi-arcs in the limit set of a singly degenerate group with bounded geometry H. Miyachi
7. On hyperbolic and spherical volumes for knot and link cone-manifolds A. D. Mednykh
8. Remarks on the curve complex, classification of surface homeomorphisms W. J. Harvey
Part II. Once-punctured tori
9. On pairs of once-punctured tori T. Jørgensen
10. Comparing two convex hull constructions for cusped hyperbolic manifolds H. Akiyoshi and M. Sakuma
11. Jørgensens picture of punctured torus groups and its refinement H. Akiyoshi, M. Sakuma, M. Wada and Y. Yamashita
12. Tetrahedral decompositions of punctured torus bundles J. R. Parker
13. On the boundary of the Earle slice for punctured torus groups Y. Komori
Part III. Related Topics
14. Variations on a theme of Horowitz J. W. Anderson
15. Complex angle scattering D. B. A. Epstein, A. Marden and V. Markovic
16. Schwarzs lemma and the Kobayashi and Carathéodory pseudometrics on complex Banach manifolds C. J. Earle, L. A. Harris, J. H. Hubbard and S. Mitra.