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
Journal ArticleDOI
The BPS spectrum of monopole operators in ABJM: towards a field theory description of the giant torus.
TL;DR: In this article, the BPS spectrum of monopole operators in ABJM theory with Chern-Simons level k,−k was studied and it was shown that the moduli space of ABJM U(n) × U(N) theory with k−k is a particular cover of the symmetric product.
Posted Content
Mapping Class Groups do not have Kazhdan's Property (T)
TL;DR: In this article, it was shown that the mapping class group of a closed oriented surface of genus at least two does not have Kazhdan's property (T) and therefore does not support T.
Journal ArticleDOI
Homotopy groups of moduli spaces of representations
TL;DR: In this paper, the authors calculate homotopy groups of the moduli spaces for representations of a compact oriented surface in the Lie groups GL ( n, C ) and U ( p, q ).
Instanton homology and symplectic xed points
TL;DR: In this paper, a new invariant for homology 3-spheres called instanton homology was discovered, which can roughly be described as the homology of a chain complex generated by the irreducible representations of the fundamental group of the Lie group SU(2).
Journal ArticleDOI
Orientability of moduli spaces of Spin(7)-instantons and coherent sheaves on Calabi–Yau 4-folds
TL;DR: In this article, it was shown that the moduli space M P Spin (7 ) ⊂ B P of irreducible Spin ( 7 ) -instanton connections on P modulo gauge, as a manifold or derived manifold, is orientable.
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).