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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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Université de la méditerraneé aix-marseille ii faculté des sciences de luminy
TL;DR: In this paper, the authors propose a novel approach to solve the problem of plagiarism in advertising.Résumé.com.augmented-video-games.com
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Tautological classes on the moduli spaces of stable maps to projective spaces
TL;DR: In this paper, the cohomology of the moduli spaces of genus zero stable maps to projective spaces is shown to be tautological in the sense that the Bialynicki-Birula stratification in the context of Gathmann's moduli space of maps with prescribed contact order to a fixed hyperplane.
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Equivariant Novikov Inequalities
Maxim Braverman,Michael Farber +1 more
TL;DR: In this paper, an equivariant generalization of the Novikov inequalities is proposed, which allows to estimate the topology of the set of critical points of a closed basic invariant form by means of twisted equalivariant cohomology.
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New polarizations on the moduli spaces and the thurston compactification of teichmüller space
TL;DR: In this article, an isotropic foliation on the moduli space of flat G-connections was constructed for a foliation F with closed leaves and with certain kinds of singularities on an oriented closed surface.
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Rank 1 character varieties of finitely presented groups
TL;DR: In this paper, the authors describe an algorithm that takes a finite presentation for F and produces a finite representation of the coordinate ring of X(F,G), where G is a rank 1 complex affine algebraic group and F is a finitely presentable discrete group.
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.
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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).