L2-Cohomology of Hyperkähler Quotients

@article{Hitchin2000L2CohomologyOH,
  title={L2-Cohomology of Hyperk{\"a}hler Quotients},
  author={N. Hitchin},
  journal={Communications in Mathematical Physics},
  year={2000},
  volume={211},
  pages={153-165}
}
  • N. Hitchin
  • Published 2000
  • Mathematics
  • Communications in Mathematical Physics
Abstract: Using an argument of Jost and Zuo, we give a criterion which implies that the L2 harmonic forms on a complete noncompact hyperkähler manifold lie in the middle dimension and are invariant under the isometry group. This is applied to various examples, and in particular gives a verification of some of the predictions of Sen on monopole moduli spaces. 
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References

SHOWING 1-10 OF 15 REFERENCES
Hyperkähler metrics and supersymmetry
We describe two constructions of hyperkähler manifolds, one based on a Legendre transform, and one on a sympletic quotient. These constructions arose in the context of supersymmetric nonlinearExpand
The cohomology of the space of magnetic monopoles
Denote byXq the reduced space ofSU2 monopoles of chargeq in ℝ3. In this paper the cohomology ofXq, the cohomology with compact supports ofXq, and the image of the latter in the former are allExpand
Instantons on Noncommutative ℝ4, and (2,0) Superconformal Six Dimensional Theory
Abstract:We show that the resolution of moduli space of ideal instantons parameterizes the instantons on noncommutative ℝ4. This moduli space appears to be the Higgs branch of the theory ofExpand
Vanishing of intersection numbers on the moduli space of Higgs bundles
In this paper we consider the topological side of a problem which is the analogue of Sen's S-duality testing conjecture for Hitchin's moduli space of rank 2 stable Higgs bundles of fixed determinantExpand
Vanishing theorems for L^2-cohomology on infinite coverings of compact Kahler manifolds and applications in algebraic geometry
In geometry, various notions of hyperbolicity have been introduced, and the appellation "hyperbolic" is intended to signify that a space shares some of the geometric properties that distinguish theExpand
Monopole and dyon bound states in N = 2 supersymmetric Yang-Mills theories
We study the existence of monopole bound states saturating the BPS bound in N = 2 supersymmetric Yang-Mills theories. We describe how the existence of such bound states relates to the topology ofExpand
Electromagnetic duality and SU(3) monopoles
Abstract We consider the low-energy dynamics of a pair of distinct fundamental monopoles that arise in the N = 4 supersymmetric SU (93) Yang-Mills theory broken to U (1) × U (1). Both the longExpand
Construction of Instantons
A complete construction, involving only linear algebra, is given for all self-dual euclidean Yang-Mills fields.
Dyon-monopole bound states, self-dual harmonic forms on the multi-monopole moduli space, and SL (2,Z) invariance in string theory
Abstract Existence of SL(2,Z) duality in toroidally compactified heterotic string theory (or in the N = 4 supersymmetric gauge theories), that includes the strong-weak coupling dualityExpand
THE SELF-DUALITY EQUATIONS ON A RIEMANN SURFACE
In this paper we shall study a special class of solutions of the self-dual Yang-Mills equations. The original self-duality equations which arose in mathematical physics were defined on EuclideanExpand
...
1
2
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