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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
Citations
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Toric structures on the moduli space of flat connections on a Riemann surface II: Inductive decomposition of the moduli space
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1992 Trieste Lectures on Topological Gauge Theory and Yang-Mills Theory
TL;DR: In this paper, a connection between Yang-Mills theory on arbitrary Riemann surfaces and two types of topological field theory, the so called $BF$ and cohomological theories, is explained.
Journal ArticleDOI
The topology of reduces phase spaces of the motion of vortices on a sphere
TL;DR: In this article, the motion of point vortices in a perfect incompressible fluid on a two-dimensional sphere can be represented by a Hamiltonian flow which is invariant under the action of the special orthogonal group SO(3).
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On the construction of perfect Morse functions on compact manifolds of coherent states
Stefan Berceanu,A. Gheorghe +1 more
TL;DR: The case of a compact, connected, simply connected Lie group of symmetry, having the same rank as the stationary group of the coherent states, such that the manifold of coherent states is a Kahlerian C-space, is considered in this article.
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{$\cal W$}-Gauge Structures and their Anomalies:An Algebraic Approach
TL;DR: In this paper, a general soldering procedure is proposed to express zero curvature conditions for the ∆-currents in terms of conformally covariant differential operators acting on the gauge fields and to obtain, at the same time, the complete nilpotent BRS differential algebra generated by ∆ −currents, gauge fields, and the ghost fields corresponding to ∆ -diffeomorphisms.
References
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Book
Principles of Algebraic Geometry
Phillip Griffiths,Joe Harris +1 more
TL;DR: In this paper, a comprehensive, self-contained treatment of complex manifold theory is presented, focusing on results applicable to projective varieties, and including discussion of the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex.
Book
Inequalities: Theory of Majorization and Its Applications
TL;DR: In this paper, Doubly Stochastic Matrices and Schur-Convex Functions are used to represent matrix functions in the context of matrix factorizations, compounds, direct products and M-matrices.
Book
Geometric Invariant Theory
TL;DR: Geometric invariant theory for moduli spaces has been studied extensively in the mathematical community as mentioned in this paper, with a large number of applications to the moduli space construction problem, see, for instance, the work of Mumford and Fogarty.
Journal ArticleDOI
Self-duality in four-dimensional Riemannian geometry
TL;DR: In this article, the authors present a self-contained account of the ideas of R. Penrose connecting four-dimensional Riemannian geometry with three-dimensional complex analysis, and apply this to the self-dual Yang-Mills equations in Euclidean 4-space and compute the number of moduli for any compact gauge group.
Journal ArticleDOI
Stable and unitary vector bundles on a compact Riemann surface
M. S. Narasimhan,C. S. Seshadri +1 more
TL;DR: In this article, it was shown that on the space of isomorphic classes of unitary vector bundles on X of a given rank, there is a natural structure of a normal projective variety (Theorem 8.1).