Instantons and Four-Manifolds (Paperback, 2, 1991. Softcover)

to the First Edition.- 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.- 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 M.- 9 The Collar Theorem.- Decay estimates.- Conformal 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 Transformations.- Appendix B The Pontrjagin-Thom Construction.- Appendix C Weitzenbock Formulas.- Appendix D The Removability of Singularities.- Appendix E Topological Remarks.