This is a collection of the works of Michael Atiyah, a well-established mathematician and winner of the Fields Medal. It is thematically divided into volumes; this one discusses gauge theory, a current topic of research. The focus of Professor Atiyah's work has been in the areas algebraic geometry and topology, but he has also had many interactions with theoretical physicists. In addition, this book includes papers of a more general nature, dealing with mathematical education and other related topics. The impetus behind this set of collected works of great mathematicians came from the Chinese American Professor S.S.Chern of Berkeley.
'Now a single book suffices to provide not only some of the standard references and proofs, but also a variety of informal survey articles which set the whole area in context ... an essential reference.'
N.J. Hitchin, Zentralblatt für Mathematik und ihre Grenzgebiete/Mathematics Abstracts
94: Deformations of instantons.
95: Instantons and algebraic geometry.
96: Construction of instantons.
97: Self-duality in four-dimensional Riemannian geometry.
98: Geometrical aspects of gauge theories.
99: Geometry of Yang-Mills fields.
100: Real and complex geometry in four dimensions.
101: Green's functions for self-dual four-manifolds.
102: Topological aspects of Yang-Mills fields.
103: Remarks on Morse theory.
104: Yang-Mills and bundles over algebraic curves.
105: The Yang-Mills equations over Riemann surfaces.
106: Convexity and commuting Hamiltonians.
107: Angular momentum, convex polyhedra and algebraic geometry.
108: Convexity and loop groups.
109: The moment map and equivariant cohomology.
110: The moment map in symplectic geometry.
111: Gauge theory and algebraic geometry.
112: The Yang-Mills equations and the structure of 4-manifolds.
113: Geometry of monopoles.
114: Solutions of classical equations in gauge theories: fundamental interactions and rigorous results.
115: Low-energy scattering of non-abelian monopoles.
116: Low-energy scattering of Non-Abelian magnetic monopoles.
117: Instantons in two and four dimensions.
118: Magnetic monopoles in hyperbolic space.
119: Anomalies and index theory.
120: Dirac operators coupled to vector potentials.
121: Topological aspects of anomalies.
122: Commentary on Manin's manuscript New dimensions in geometry.
123: Eigenvalues of the Dirac operator.
124: Circular symmetry and stationary-phase approximation.