Gauge Theory: an Introduction

Claudio Bartocci


- Principal bundles and connections
- Curvature, holonomy, characteristic classess

- The space of connections and the gauge group
- The space of gauge equivalence classes of connections and its local structure

- Yang-Mills and ASD equations
- The basic instanton on S^4
- The local structure of the moduli space
- Orientability
- Uhlenbeck's compactification of moduli spaces

- Periodic instantons and Nahm transforms

Basic References
- S.K. Donaldson & P.B. Kronheimer, The Geometry of Four-Manifolds, Clarendon Press, Oxford 1990
- D.S. Freed & K.K. Uhlenbeck, Instantons and Four-Manifolds, Springer-Verlag, New York 1984
- Gauge Theory and the Topology of Four-Manifolds, R. Friedman & J.W. Morgan eds., IAS/Park City Mathematics Series vol. 4, American Mathematical Society and Institute for Advanced Study, 1998

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