Preface Reader's Advisory Ch. 1. What Is a Manifold? 3 Ch. 2. Hyperbolic Geometry and Its Friends 43 Ch. 3. Geometric Manifolds 109 Ch. 4. The Structure of Discrete Groups 209 Glossary 289… Expand

1. A conjectural picture of 3-manifolds. A major thrust of mathematics in the late 19th century, in which Poincare had a large role, was the uniformization theory for Riemann surfaces: that every… Expand

This article was widely circulated as a preprint, about 12 years ago. At that time the Bulletin did not accept research announcements, and after a couple of attempts to publish it, I gave up, and the… Expand

Introduction. Mappings from an interval to itself provide the simplest possible examples of smooth dynamical systems. Such mappings have been widely studied in recent years since they occur in quite… Expand

This paper develops a theory of Lipschitz comparisons of hyperbolic surfaces
analogous to the theory of quasi-conformal comparisons. Extremal Lipschitz maps (minimal
stretch maps) and geodesics for… Expand

This is a construction of closed symplectic manifolds with no Kaehler structure. A symplectic manifold is a manifold of dimension 2k with a closed 2-form a such that ak is nonsingular. If M2k is a… Expand

Our main theorem is that, if M is a closed hyperbolic 3-manifold which fibres over the circle with hyperbolic fibre S and pseudo-Anosov monodromy, then the lift of the inclusion of S in M to… Expand