Contents

pp v-vi

Contributors

pp vii-vii

Names of Participants

pp viii-viii

Introduction

pp ix-xiii

Acknowledgements

pp xiv-xiv

PART 1 - SYMPLECTIC GEOMETRY

pp 1-2

Introduction

pp 3-6

Rational and ruled symplectic 4-manifolds

pp 7-14

Symplectic capacities

pp 15-34

The nonlinear Maslov index

pp 35-44

Filling by holomorphic discs and its applications

pp 45-68

PART 2 - JONES/WITTEN THEORY

pp 69-70

Introduction

pp 71-72

New results in Chern-Simons theory

pp 73-96

Geometric quantization of spaces of connections

pp 97-100

Evaluations of the 3-manifold invariants of Witten and Reshetikhin-Turaev for sl(2, C)

pp 101-114

Representations of braid groups

pp 115-122

PART 3 - THREE-DIMENSIONAL MANIFOLDS

pp 123-124

Introduction

pp 125-126

An introduction to polyhedral metrics of non-positive curvature on 3-manifolds

pp 127-162

Finite groups of hyperbolic isometries

pp 163-176

Pin structures on low-dimensional manifolds

pp 177-242