Instantons and Four-Manifolds

Instantons and Four-Manifolds by D. S. Freed, K. K. Uhlenbeck.

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...

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Bibliographic Details
Main Authors: Freed, D. S. (Author), Uhlenbeck, K. K. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY : Springer New York : Imprint: Springer, 1984.
Edition:1st ed. 1984.
Series:Mathematical Sciences Research Institute Publications, 1
Springer eBook Collection.
Subjects:
Manifolds (Mathematics).
Complex manifolds.
Mathematical analysis.
Analysis (Mathematics).
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
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.

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