A New Foreword

Summary

The article “Notes on Notes of Thurston” was intended as an exposition of some portions of Thurston's lecture notes The Geometry and Topology of Three-Manifolds. The work described in Thurston's lecture notes revolutionized the study of Kleinian groups and hyperbolic manifolds, and formed the foundation for parts of Thurston's proof of his Geometrization theorem. At the time, much of the material in those Notes was unavailable in a published form. In this foreword, we point the reader to some more recent publications where detailed explanations of the material in Thurston's original lecture notes are available. We will place a special emphasis on Thurston's Chapters 8 and 9. This material was the basis for much of our original article and it still represents the part least well-digested by the mathematical community. This is also the material which has been closest to the author's subsequent interests, so the selection will, by necessity, reflect some of his personal biases.

We hope this foreword will be useful to students and working mathematicians who are attempting to come to grips with the very beautiful, but also sparingly described, mathematics in Thurston's notes. No attempt has been made to make this foreword self-contained. It is simply a rough-and-ready guide to some of the relevant literature. In particular, we will not have space to define all the mathematical terms used, but we hope the reader will make use of the many references to sort these out. In particular, we will assume that the reader has a copy of Thurston's notes on hand.