作者：（德）康拉德·P.思科贝尔
页数：134
出版社：哈尔滨工业大学出版社
出版日期：2021
ISBN：9787560394824
电子书格式：pdf/epub/txt
内容简介
本书是一部英文版的数学专著，在本书中我们研究在黎曼紧四维流形上具有定相交形式和非平庸贝蒂数的PU(2)瞬子模空间.我们将从拓扑、黎曼流形及当背景流形是复平面时复几何的角度来研究这些模空间,这样的模空间包含一个b1维圆环的有限交作为奇点,即U(1)可约连通的一个分量。
目录
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
编辑手记
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
编辑手记
