Description
Book SynopsisOffers a perspective on how 4-manifold theory was studied before the discovery of modern-day Seiberg-Witten theory. This book predates Donaldson's applications of the subject to 4-manifold topology, where the central concern was the geometry of the moduli space.
Table of ContentsGeometric invariant theory and the moduli of bundles: Geometric invariant theory by D. Gieseker The numerical criterion by D. Gieseker The moduli of stable bundles by D. Gieseker References by D. Gieseker Anti-self-dual connections and stable vector bundles: Hermitian bundles, Hermitian connections and their curvatures by J. Li Hermitian-Einstein connections and stable vector bundles by J. Li The existence of Hermitian-Einstein metrics by J. Li References by J. Li An introduction to gauge theory: The context of Gauge theory by J. W. Morgan Principal bundles and connections by J. W. Morgan Curvature and characteristic classes by J. W. Morgan The space of connections by J. W. Morgan The ASD equations and the moduli space by J. W. Morgan Compactness and gluing theorems by J. W. Morgan The Donaldson polynomial invariants by J. W. Morgan The connected sum theorem by J. W. Morgan References by J. W. Morgan Computing Donaldson invariants: Overview by R. J. Stern -2 spheres and the blowup formula by R. J. Stern Simple-type criteria and elliptic surfaces by R. J. Stern Elementary rational blowdowns by R. J. Stern Taut configurations and Horikowa surfaces by R. J. Stern References by R. J. Stern Donaldson-Floer theory: Introduction by C. Taubes and J. A. Bryan Quantization by C. Taubes and J. A. Bryan Simplicial decomposition of $\Cal{M}^0_X$ by C. Taubes and J. A. Bryan Half-infinite dimensional spaces by C. Taubes and J. A. Bryan References by C. Taubes and J. A. Bryan.
