Journal ArticleDOI
The Yang-Mills equations over Riemann surfaces
Michael Atiyah,Raoul Bott +1 more
Reads0
Chats0
TLDR
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
More filters
Book ChapterDOI
On the cohomology of moduli spaces of rank two vector bundles over curves
Don Zagier,Don Zagier +1 more
TL;DR: In this article, a moduli space of stable n-dimensional vector bundles over a Riemann surface with determinant bundle Λ n (E) ≡ L is introduced, which can be compactified by the addition of semi-stable bundles to a projective, but in general singular, variety N c,n,L.
Journal ArticleDOI
Chirality change in string theory
TL;DR: In this paper, it is shown that string theory compactifications leading to low energy effective theories with different chiral matter content are connected through phase transitions, described by non-trivial quantum fixed point theories.
Posted Content
Equivariant Verlinde formula from fivebranes and vortices
Sergei Gukov,Sergei Gukov,Du Pei +2 more
TL;DR: In this paper, the authors show that complex Chern-Simons theory on a Seifert manifold is equivalent to a topologically twisted supersymmetric theory and its partition function can be naturally regularized by turning on a mass parameter.
Journal ArticleDOI
Convergence properties of the Yang-Mills flow on Kaehler surfaces
TL;DR: In this article, the Yang-Mills flow on a compact Kahler surface with Kahler form was shown to converge to the double dual of the graded sheaf associated to the Harder-Narasimhan-Seshadri filtration of the holomorphic bundle.
Posted Content
Mapping class group dynamics on surface group representations
TL;DR: In this paper, the authors summarize known results and state open questions about the properness of the mapping class group's actions in a Lie group and show that if G is compact, the actions are ergodic, while G is noncompact, the associated deforma- tion space contains open subsets containing the Fricke-Teichmuller space upon which Modacts properly.
References
More filters
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).