Preface 2005

Summary

In 1987 Cambridge University Press published the proceedings of meetings in Warwick and Durham as Lecture Notes 111 and 112. The original preface is reprinted above. Taking account of demand, CUP suggested that certain of the articles in the original two volumes be reprinted. We have chosen four of them to comprise a single new volume. We believe they will continue to be helpful to those learning about the field. The authors have kindly given permission to reissue their work.

Prt I, “Notes on Notes …” (N&N), has a newforeword by Canary. Particular topics in Chapters 8 and 9 of Thurston's original lecture notes had formed the basis for much of N&N. Still, there is other important material in those chapters that has not been widely digested by the mathematical community at large, yet has turned out to play key roles in later developments. The purpose of the foreword is to provide a guide to the recent literature where explanations of this additional material are now available. Also included are brief accounts of the recently announced solutions of the tameness and ending lamination conjectures, direct generalizations of topics in those fateful chapters.

Likewise, in Part II, the centrality of the convex core in studying hyperbolic manifolds has become even more apparent in the intervening years as important additional details of its structure have been worked out. Accordingly, the careful account of this topic given in the original article on convex hulls and Sullivan's theorem has been brought up to date with a new addendum by Epstein and Marden.