Preface

Summary

This volume forms the proceedings of the workshop Kleinian Groups and Hyperbolic 3-Manifolds which was held at the Mathematics Institute, University of Warwick, 11–15 September 2001. Almost 80 people took part, many travelling large distances to come.

The workshop was organised around six expository lectures by Yair Minsky on the combinatorial part of his programme to extend his results on Thurston's ending lamination conjecture for once punctured tori to general surfaces. Not long after the workshop, a complete proof of the conjecture was announced by Brock, Canary and Minsky. This is undoubtedly one of the most important developments in the subject in the last decade, paving the way for a complete understanding of the internal geometry of hyperbolic 3-manifolds, and involving deep understanding of the fascinating links between this geometry and the combinatorics of the curve complex. Minsky's lectures, reproduced in this volume, give an invaluable overview.

As was clear from the talks at the conference, hyperbolic geometry is currently developing with astonishing rapidity. We hope that the expositions here will provide a useful guide. The volume is divided into three parts. Part I contains Minsky's lectures together with other articles on the geometry of hyperbolic 3-manifolds. The paper by Hodgson and Kerckhoff is an exposition of their recent work on cone manifolds. This is key to many recent developments, in particular Brock and Bromberg's proof, outlined here, of the long standing Bers' density conjecture for incompressible ends. Otal's result on unknottedness is an important ingredient.