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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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Covariant W gravity and its moduli space from gauge theory
Jan de Boer,Jacob K. Goeree +1 more
TL;DR: In this paper, the covariant action of WZW is shown to be a Legendre transform of the WW action, and the same general formula provides a geometrical interpretation of W transformations: they are just a homotopy contraction of ordinary gauge transformations.
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Holomorphic Principal Bundles Over Elliptic Curves II: The Parabolic Construction
Robert Friedman,John W. Morgan +1 more
TL;DR: In this article, the moduli space of holomorphic semistable principal G-bundles over an elliptic curve is constructed by considering deformations of a minimally unstable G bundle, and the set of all such deformations can be described as the C^* quotient of the cohomology group of a sheaf of unipotent groups.
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Schur and Schubert polynomials as Thom polynomials-cohomology of moduli spaces
László M. Fehér,Richárd Rimányi +1 more
TL;DR: In this article, the theory of Schur and Schubert polynomials is revisited from the point of view of generalized Thom polynomial solutions of interpolation problems.
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The evaluation map in field theory, sigma-models and strings. II
TL;DR: The role of the evaluation map in the calculations of global anomalies is discussed in this article, both for field theories and for sigma-models, and it is shown that global anomalies are connected with the differential characters of Cheeger and Simons.
Journal ArticleDOI
Relations in the cohomology ring of the moduli space of rank 2 Higgs bundles
TL;DR: In this paper, the rational cohomology ring of 7-n when the rank is 2 and the degree is odd is characterized and a complete set of generators for this ring is given.
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).