Corpus ID: 119313729

G2 instantons and the Seiberg-Witten monopoles

@article{Haydys2017G2IA,
  title={G2 instantons and the Seiberg-Witten monopoles},
  author={Andriy Haydys},
  journal={arXiv: Differential Geometry},
  year={2017}
}
  • Andriy Haydys
  • Published 2017
  • Mathematics, Physics
  • arXiv: Differential Geometry
I describe a relation (mostly conjectural) between the Seiberg-Witten monopoles, Fueter sections, and G2 instantons. In the last part of this article I gathered some open questions connected with this relation. 

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References

SHOWING 1-10 OF 27 REFERENCES
A compactness theorem for the Seiberg–Witten equation with multiple spinors in dimension three
We prove that a sequence of solutions of the Seiberg–Witten equation with multiple spinors in dimension three can degenerate only by converging (after rescaling) to a Fueter section of a bundle ofExpand
$G_2$-instantons, associative submanifolds, and Fueter sections
We give a sufficient condition for an associative submanifold in a G2-manifold to appear as the bubbling locus of a sequence of G2-instantons, related to the existence of a Fueter section of a bundleExpand
On the construction of some complete metrics with exceptional holonomy
On construit explicitement trois metriques completes distinctes d'holonomie egale a G 2 , une metrique complete d'holonomie egale a Spin(7) et diverses metriques incompletes d'holonomie exceptionnelle
Gauge Theory in higher dimensions, II
The main aim of the paper is to develop the "Floer theory" associated to Calabi-Yau 3-folds, exending the analogy of Thomas' "holomorphic Casson invariant". The treatment in the body of the paper isExpand
Gauge theory, calibrated geometry and harmonic spinors
  • Andriy Haydys
  • Computer Science, Mathematics
  • J. Lond. Math. Soc.
  • 2012
TLDR
It is shown that higher dimensional anti-self-duality equations on the total spaces of spinor bundles over low-dimensional manifolds can be interpreted as the Taubes–Pidstrygach generalization of the Seiberg–Witten equations. Expand
Metrics with exceptional holonomy
It is proved that there exist metrics with holonomy G2 and Spin(7), thus settling the remaining cases in Berger's list of possible holonomy groups. We first reformulate the "holonomy H" condition asExpand
A Tour of Exceptional Geometry
A discussion of G 2 and its manifestations is followed by the definition of various groups acting on R 8 . Calculation of exterior and covariant derivatives is carried out for a specific metric on aExpand
Compactness theorems for SL(2;C) generalizations of the 4-dimensional anti-self dual equations, Part I
Uhlenbeck's compactness theorem can be used to analyze sequences of connections with anti-self dual curvature on principal SU(2) bundles over oriented 4-dimensional manifolds. The theorems in thisExpand
Twisted connected sums and special Riemannian holonomy
We give a new, connected-sum-like construction of Riemannian metrics with special holonomy G_2 on compact 7-manifolds. The construction is based on a gluing theorem for appropriate elliptic partialExpand
Connections withLP bounds on curvature
We show by means of the implicit function theorem that Coulomb gauges exist for fields over a ball inRn when the integralLn/2 field norm is sufficiently small. We then are able to prove a weakExpand
...
1
2
3
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