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Journal Article
The Yang-Mills Equations over Riemann Surfaces
M. F. Atiyah and R. Bott
Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
Vol. 308, No. 1505 (Mar. 17, 1983), pp. 523-615
Published
by: Royal Society
https://www.jstor.org/stable/37156
Page Count: 93
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Topics: Riemann surfaces, Mathematical vectors, Morse theory, Lie groups, Eigenvalues, Automorphisms, Polynomials
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Abstract
The Yang-Mills functional over a Riemann surface is studied from the point of view of Morse theory. The main result is that this is a `perfect' functional provided due account is taken of its gauge symmetry. This enables topological conclusions to be drawn about the critical sets and leads eventually to information about the moduli space of algebraic bundles over the Riemann surface. This in turn depends on the interplay between the holomorphic and unitary structures, which is analysed in detail.
Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
© 1983 Royal Society