Cyclic Higgs bundles and the affine Toda equations

DOI10.1007/s10711-014-0003-2zbMath1321.53027arXiv1011.6421OpenAlexW1979066087MaRDI QIDQ2256249

David Baraglia

Publication date: 19 February 2015

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1011.6421

zbMATH Keywords

harmonic mapToda equationHiggs bundlecyclic bundle

Mathematics Subject Classification ID

Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) (53C07) Differential geometric aspects of harmonic maps (53C43)

Related Items (13)

Maximal \(\mathsf{Sp}(4,\mathbb R)\) surface group representations, minimal immersions and cyclic surfaces ⋮ Parabolic Higgs bundles and cyclic monopole chains ⋮ Topological-antitopological fusion and the quantum cohomology of Grassmannians ⋮ Cyclic Higgs bundles and minimal surfaces in pseudo-hyperbolic spaces ⋮ Hitchin components for orbifolds ⋮ Correlation of the renormalized Hilbert length for convex projective surfaces ⋮ Length spectrum compactification of the \(\mathrm{SO}_0(2, 3)\)-Hitchin component ⋮ Generalized Kazdan-Warner equations associated with a linear action of a torus on a complex vector space ⋮ Cyclic surfaces and Hitchin components in rank 2 ⋮ Variations along the Fuchsian locus ⋮ Twisted cyclic quiver varieties on curves ⋮ The moduli spaces of equivariant minimal surfaces in \({\mathbb {RH}}^3\) and \(\mathbb {RH}^4\) via Higgs bundles ⋮ Kostant, Steinberg, and the Stokes matrices of the tt*-Toda equations

Cites Work

• Holomorphic curves and Toda systems
• Two-dimensional generalized Toda lattice
• Lie groups and Teichmüller space
• Lectures on real semisimple Lie algebras and their representations
• Exactly and completely integrable nonlinear dynamical systems
• Geometry of Higgs and Toda fields on Riemann surfaces
• Nonlinear \(\sigma\)-models on spheres and Toda systems
• The Principal Three-Dimensional Subgroup and the Betti Numbers of a Complex Simple Lie Group
• The Self-Duality Equations on a Riemann Surface
• Constructing Variations of Hodge Structure Using Yang-Mills Theory and Applications to Uniformization
• Harmonic maps and periodic Toda systems
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