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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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Equivariant smooth Deligne cohomology
TL;DR: In this paper, a notion of equivariant smooth Deligne cohomology group is introduced, which is a generalization of both ordinary smooth Deligna cohomologies and ordinary equivariants.
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Lectures on Representations of Surface Groups
TL;DR: HAL as mentioned in this paper is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not, which may come from teaching and research institutions in France or abroad, or from public or private research centers.
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Twisted K-Homology and Group-Valued Moment Maps
TL;DR: In this article, a functor from prequantized quasi-Hamiltonian G-spaces (M,ω,Φ) at level k to the fusion ring (Verlinde algebra) R k (G) is defined as a push forward in twisted equivariant K-homology.
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Localization for nonabelian group actions
Lisa C. Jeffrey,Frances Kirwan +1 more
TL;DR: Theorem 8.1.1, the residue formula, was proved in this article for the fundamental class of a compact symplectic manifold in terms of the degree of the dimension of the manifold.
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Covariant $W$ Gravity \& its Moduli Space from Gauge Theory
Jan de Boer,Jacob K. Goeree +1 more
TL;DR: In this paper, the covariant action of the WZW action is shown to be a Fourier transform of the regular WW action and the moduli space relevant to gravity is part of the modulus space of the G-bundles over a Riemann surface.
References
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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).