Contents

pp v-viii

Preface

pp ix-x

Part One - Poisson geometry and morita equivalence

pp 1-2

1 - Introduction

pp 3-4

2 - Poisson geometry and some generalizations

pp 5-24

3 - Algebraic Morita equivalence

pp 25-36

4 - Geometric Morita equivalence

pp 37-66

5 - Geometric representation equivalence

pp 67-71

Bibliography

pp 72-78

Part Two - Formality and star products

pp 79-80

1 - Introduction

pp 81-86

2 - The star product

pp 87-92

3 - Rephrasing the main problem: the formality

pp 93-112

4 - Digression: what happens in the dual

pp 113-119

5 - The Kontsevich formula

pp 120-133

6 - From local to global deformation quantization

pp 134-140

Bibliography

pp 141-144

Part Three - Lie groupoids, sheaves and cohomology

pp 145-146

1 - Introduction

pp 147-148

2 - Lie groupoids

pp 149-174

3 - Sheaves on Lie groupoids

pp 175-209

4 - Sheaf cohomology

pp 210-241

5 - Compactly supported cohomology

pp 242-268

Bibliography

pp 269-272

Part Four - Geometric methods in representation theory

pp 273-274

1 - Reductive Lie Groups: Definitions and Basic Properties

pp 275-281

2 - Compact Lie Groups

pp 282-293

3 - Representations of Reductive Lie Groups

pp 294-304

4 - Geometric Constructions of Representations

pp 305-320