IAS/Park City Mathematics Series 1998; 221 pp; hardcover Volume: 4 ISBN10: 0821805916 ISBN13: 9780821805916 List Price: US$47 Member Price: US$37.60 Order Code: PCMS/4
 The lectures in this volume provide a perspective on how 4manifold theory was studied before the discovery of modernday SeibergWitten theory. One reason the progress using the SeibergWitten invariants was so spectacular was that those studying \(SU(2)\)gauge theory had more than ten years' experience with the subject. The tools had been honed, the correct questions formulated, and the basic strategies well understood. The knowledge immediately bore fruit in the technically simpler environment of the SeibergWitten theory. Gauge theory long predates Donaldson's applications of the subject to 4manifold topology, where the central concern was the geometry of the moduli space. One reason for the interest in this study is the connection between the gauge theory moduli spaces of a Kähler manifold and the algebrogeometric moduli space of stable holomorphic bundles over the manifold. The extra geometric richness of the \(SU(2)\)moduli spaces may one day be important for purposes beyond the algebraic invariants that have been studied to date. It is for this reason that the results presented in this volume will be essential. Titles in this series are copublished with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price. Readership Graduate students and research mathematicians working in algebraic geometry. Table of Contents Geometric invariant theory and the moduli of bundles  D. Gieseker  Geometric invariant theory
 D. Gieseker  The numerical criterion
 D. Gieseker  The moduli of stable bundles
 D. Gieseker  References
Antiselfdual connections and stable vector bundles  J. Li  Hermitian bundles, Hermitian connections and their curvatures
 J. Li  HermitianEinstein connections and stable vector bundles
 J. Li  The existence of HermitianEinstein metrics
 J. Li  References
An introduction to gauge theory  J. W. Morgan  The context of Gauge theory
 J. W. Morgan  Principal bundles and connections
 J. W. Morgan  Curvature and characteristic classes
 J. W. Morgan  The space of connections
 J. W. Morgan  The ASD equations and the moduli space
 J. W. Morgan  Compactness and gluing theorems
 J. W. Morgan  The Donaldson polynomial invariants
 J. W. Morgan  The connected sum theorem
 J. W. Morgan  References
Computing Donaldson invariants  R. J. Stern  Overview
 R. J. Stern  2 spheres and the blowup formula
 R. J. Stern  Simpletype criteria and elliptic surfaces
 R. J. Stern  Elementary rational blowdowns
 R. J. Stern  Taut configurations and Horikowa surfaces
 R. J. Stern  References
DonaldsonFloer theory  C. Taubes and J. A. Bryan  Introduction
 C. Taubes and J. A. Bryan  Quantization
 C. Taubes and J. A. Bryan  Simplicial decomposition of \(\Cal{M}^0_X\)
 C. Taubes and J. A. Bryan  Halfinfinite dimensional spaces
 C. Taubes and J. A. Bryan  References
