Cover Image
Read Now

Instantons and Four-Manifolds

This book is the outcome of a seminar organized by Michael Freedman and Karen Uhlenbeck (the senior author) at the Mathematical Sciences Research Institute in Berkeley during its first few months of existence. Dan Freed (the junior author) was originally appointed as notetaker. The express purpose o...

Full description

Bibliographic Details
Main Authors: Freed, D. S., Uhlenbeck, K. K. (Author)
Format: eBook
Language:English
Published: New York, NY Springer New York 1984, 1984
Edition:1st ed. 1984
Series:Mathematical Sciences Research Institute Publications
Subjects:
Mathematical Analysis
Analysis
Manifolds And Cell Complexes
Manifolds (mathematics)
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • §1 Fake ?4
  • Differentiable structures
  • Topological 4-manifolds
  • Differentiable 4-manifolds
  • A surgical failure
  • §2 The Yang-Mills Equations
  • Connections
  • Topological quantum numbers
  • The Yang-Mills functional
  • Line bundles
  • Donaldson’s Theorem
  • §3 Manifolds of Connections
  • Sobolev spaces
  • Reducible connections
  • A slice theorem
  • The parametrized moduli space
  • The moduli space
  • §4 Cones on ??2
  • Slices again
  • Structure of the singular point
  • Perturbing the metric
  • §5 Orientability
  • Index bundles
  • Components of J
  • The element -1
  • §6 Introduction to Taubes’ Theorem
  • Instantons on S4
  • A grafting procedure
  • Tools from analysis
  • Analytic properties of SDYME
  • §7 Taubes Theorem
  • Blowing up the metric
  • The eigenvalue estimate
  • The linearized equation
  • Taubes’ projection
  • §8 Compactness
  • Compactness and regularity
  • Measuring concentrated curvature
  • Compactness in ?
  • §9 The Collar Theorem
  • Decay estimates
  • Conformai deformations
  • Exponential gauges
  • Connectivity of the collar
  • §10 The Technique of Fintushel and Stern
  • The moduli space for SO(3) bundles
  • Reducible connections
  • Analytic details
  • Appendix A The Group of Sobolev Gauge sTransformations
  • Appendix B The Pontrjagin-Thom Construction
  • Appendix C Weitzenböck Formulas
  • Appendix D The Removability of Singularities
  • Appendix E Topological Remarks

Similar Items