MOMENT MAPS, COBORDISMS, AND HAMILTONIAN GROUP ACTIONS

By MARY LEE

CONTENTS CHAPTER 1 INTRODUCTION 1 TOPOLOGICAL ASPECTS OF HAMILTONIAN GROUP ACTIONS 2 HAMILTONIAN COBORDISM 3 THE LINEARIZATION THEOREM AND NON-COMPACT COBORDISMS 4 ABSTRACT MOMENT MAPS AND NON-DEGENERACY 5 THE QUANTUM LINEARIZATION THEOREM AND ITS APPLICATIONS 6 ACKNOWLEDGEMENTS PART 1 COBORDISM CHAPTER 2 HAMILTONIAN COBORDISM 1 HAMILTONIAN GROUP ACTIONS 2 HAMILTONIAN GEOMETRY 3 COMPACT HAMILTONIAN COBORDISMS 4 PROPER HAMILTONIAN COBORDISMS 5 HAMILTONIAN COMPLEX COBORDISMS CHAPTER 3 ABSTRACT MOMENT MAPS 1 ABSTRACT MOMENT MAPS: DE?NITIONS AND EXAMPLES 2 PROPER ABSTRACT MOMENT MAPS 3 COBORDISM 4 FIRST EXAMPLES OF PROPER COBORDISMS 5 COBORDISMS OF SURFACES 6 COBORDISMS OF LINEAR ACTIONS CHAPTER 4 THE LINEARIZATION THEOREM 1 THE SIMPLEST CASE OF THE LINEARIZATION THEOREM 2 THE HAMILTONIAN LINEARIZATION THEOREM 3 THE LINEARIZATION THEOREM FOR ABSTRACT MOMENT MAPS 4 LINEAR TORUS ACTIONS 5 THE RIGHT-HAND SIDE OF THE LINEARIZATION THEOREMS 6 THE DUISTERMAAT-HECKMAN AND GUILLEMIN-LERMAN-STERNBERG FORMULAS CHAPTER 5 REDUCTION AND APPLICATIONS 1 (PRE-)SYMPLECTIC REDUCTION 2 REDUCTION FOR ABSTRACT MOMENT MAPS 3 THE DUISTERMAAT–HECKMAN THEOREM 4 K¨AHLER REDUCTION 5 THE COMPLEX DELZANT CONSTRUCTION 6 COBORDISM OF REDUCED SPACES 7 JE?REY–KIRWAN LOCALIZATION 8 CUTTING PART 2 QUANTIZATION CHAPTER 6 GEOMETRIC QUANTIZATION 1 QUANTIZATION AND GROUP ACTIONS 2 PRE-QUANTIZATION 3 PRE-QUANTIZATION OF REDUCED SPACES 4 KIRILLOV–KOSTANT PRE-QUANTIZATION 5 POLARIZATIONS, COMPLEX STRUCTURES, AND GEOMETRIC QUANTIZATION 6 DOLBEAULT QUANTIZATION AND THE RIEMANN–ROCH FORMULA 7 STABLE COMPLEX QUANTIZATION AND SPINC QUANTIZATION 8 GEOMETRIC QUANTIZATION AS A PUSH-FORWARD CHAPTER 7 THE QUANTUM VERSION OF THE LINEARIZATION THEOREM 1 THE QUANTIZATION OF CD 2 PARTITION FUNCTIONS 3 THE CHARACTER OF Q(CD) 4 A QUANTUM VERSION OF THE LINEARIZATION THEOREM CHAPTER 8 QUANTIZATION COMMUTES WITH REDUCTION 1 QUANTIZATION AND REDUCTION COMMUTE 2 QUANTIZATION OF STABLE COMPLEX TORIC VARIETIES 4 STRAIGHTENING THE SYMPLECTIC AND COMPLEX STRUCTURES 5 PASSING TO HOLOMORPHIC SHEAF COHOMOLOGY 6 COMPUTING GLOBAL SECTIONS; THE LIT SET 7 THE ?CECH COMPLEX 8 THE HIGHER COHOMOLOGY 9 SINGULAR [Q,R]=0 FOR NON-SYMPLECTIC HAMILTONIAN G-MANIFOLDS 10 OVERVIEW OF THE LITERATURE