負定相交形式流形上的瞬子模空間幾何(英文)

General introduction
Part I The Geometry of PU(2)-Instanton Moduli Spaces over Manifolds with Negative Definite Intersection Form
Introduction

1 Preliminaries
1.1 The moduli space and invariants
1.2 SU(2),SO(3) and PU(2) moduli spaces
1.3 The moduli space of ASD-connections on a line bundle
1.4 Local model
1.5 Irreducibility
1.6 Regularity
1.7 Expected dimension
1.8 Compactness and orientability
1.9 Universal bundle and Donaldson u-classes
1.10 The parametrised moduli space
1.11 The Z2-metric

2 A problem in finite dimensional Riemannian geometry
2.1 The Groisser-Parker reduction
2.2 The problem
2.3 A slice of the action
2.4 The conical structure around the singular locus
2.5 The Sasaki metric in the total space of a vector bundle
2.6 The asymptotic of the metric

3 Index computations
3.1 Pontryagin classes and Donaldson μ-classes
3.2 Triviality of the projective bundle

4 Applications
Part II Moduli Spaces of PU(2)-Instantons on Minimal Class VII Surfaces with b2=1
Introduction
1 Minimal class VII surfaces with b2=1
2 Filtrable holomorphic bundles
3 The local structure of the moduli space
4 Stability
5 The boundary of the moduli space of polystable bundles
6 Non-filtrable holomorphic bundles
7 The moduli spaces
Acknowledgements
Bibliography
編輯手記