Cyclic Higgs bundles and the affine Toda equations

Details Cyclic Higgs bundles and the affine Toda equations Cyclic Higgs bundles and the affine Toda equations

2010-11-30

arxiv.org/abs/1011.6421v3

Mathematics

Differential Geometry

23 pages

Scientific paper

We introduce a class of Higgs bundles called cyclic which lie in the Hitchin
component of representations of a compact Riemann surface into the split real
form of a simple Lie group. We then prove that such a Higgs bundle is
equivalent to a certain class of solutions to the affine Toda equations. We
further explain this relationships in terms of lifts of harmonic maps.

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