Journal ArticleDOI
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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Journal ArticleDOI
Cohomology of certain moduli spaces of vector bundles
TL;DR: The third and fourth cohomology groups of as discussed by the authors are torsion-free, and the third and four cohomologies of the first and the fourth cohoms of the second and the fifth cohoms, respectively, have been constructed by Seshadri [17] and as discussed by the authors.
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Non-Abelian Localization For Chern-Simons Theory
Chris Beasley,Edward Witten +1 more
TL;DR: In this paper, the authors show that the partition function of Chern-Simons theory admits a topological interpretation in terms of the equivariant cohomology of the moduli space of flat connections on a Seifert manifold.
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The equivariant cohomology of hypertoric varieties and their real loci
Megumi Harada,Tara S. Holm +1 more
TL;DR: In this article, the authors give a combinatorial description of the T-equivariant cohomology of a Hamiltonian T space with a proper moment map, bounded below in some component.
Journal ArticleDOI
Projective structures, flat bundles, and kähler metrics on moduli spaces
Abstract: This paper deals mainly with the geometrical and topological aspects of the connection recently discovered by Zograf and Takhtadzhyan between the accessory parameters of Schwarzian differential equations and the Weil-Petersson metric on Teichmuller space. In addition it is shown that there is an analogous effect in the theory for flat bundles.Bibliography: 23 titles.
Book ChapterDOI
Lectures on the Moduli Stack of Vector Bundles on a Curve
TL;DR: In this article, the moduli stack of vector bundles on an algebraic curve is used as an example for algebraic stacks and a short course on algebraic moduli stacks is presented.
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).