Michael Atiyah: Collected Works: Volume 5: Gauge Theories

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Editorial Reviews

From the Publisher

"It is a welcome turn of events that Sir Michael has been talked into producing this edition of his collected works now, even though his mathematical career shows no signs of abating. We may expect that a complete edition of his mathematical opus will eventually require at least an extra volume. The advantage of the present arrangement is that we are provided not only with an extremely useful and timely compendium of the books and articles of this profound and influential thinker, but also with this own reflections on their origins, interrelations and place in the mathematical activity of the time. . . . Atiyah is one of the great mathematical teachers of our time. These papers are therefore not only of lasting importance, but are in addition, a true pleasure to read. The appearance of these volumes is thus an occasion for rejoicing." --American Scientist

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Product Details

  • ISBN-13: 9780198532798
  • Publisher: Oxford University Press, USA
  • Publication date: 6/30/1988
  • Pages: 710
  • Product dimensions: 10.00 (w) x 7.69 (h) x 1.66 (d)

Table of Contents

PART VI: Gauge Theories
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 Theory
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
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 of Manin's Manuscript "New Dimensions in Geometry"
123. Eigenvalues of the Dirac Operator
124. Circular Symmetry and Stationary-Phase Approximation

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