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The Yang-Mills equations over Riemann surfaces
Michael Atiyah,Raoul Bott +1 more
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In this article, the Yang-Mills functional over a Riemann surface is studied from the point of view of Morse theory, and the main result is that this is a perfect 9 functional provided due account is taken of its gauge symmetry.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 ‘perfect9 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.read more
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Quantum field theory and the Jones polynomial
TL;DR: In this paper, it was shown that 2+1 dimensional quantum Yang-Mills theory with an action consisting purely of the Chern-Simons term is exactly soluble and gave a natural framework for understanding the Jones polynomial of knot theory in three dimensional terms.
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Seiberg-Witten Prepotential from Instanton Counting
TL;DR: In this article, a two-parameter generalization of the Seiberg-Witten prepotential is presented, which is rather natural from the M-theory/five dimensional perspective, and conjecture its relation to the tau-functions of KP/Toda hierarchy.
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The self-duality equations on a riemann surface
TL;DR: In this paper, the authors studied a special class of solutions of the self-dual Yang-Mills equations on Riemann surfaces and showed that the moduli space of all solutions turns out to be a manifold with an extremely rich geometric structure.
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Anti Self‐Dual Yang‐Mills Connections Over Complex Algebraic Surfaces and Stable Vector Bundles
TL;DR: In this paper, a correspondance entre the geometries algebrique and the geometry differentielle des fibres vectoriels is presented, and a connexion irreductible d'Hermite-Einstein par rapport a metrique ω.
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The moment map and equivariant cohomology
TL;DR: In this article, the authors propose a solution to solve the problem of spamming, which is called spamming-based spamming.$$$/$/$/$/$$
References
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Vector Bundles Over an Elliptic Curve
TL;DR: In this article, the authors studied vector bundles over an algebraically closed field k and proved that the vector bundles are a direct sum of line-bundles over the field k. The results are valid in both characteristic 0 and p.
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Convexity and Commuting Hamiltonians
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Some remarks on the Gribov ambiguity
TL;DR: In this article, the set of all connections of a principal bundle over the 4-sphere with compact nonabelian Lie group under the action of the group of gauge transformations is studied.
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Connections with l**p bounds on curvature
TL;DR: In this paper, it was shown by means of the implicit function theorem that Coulomb gauges exist for fields over a ball over compact manifolds when the integral field norm is sufficiently small.