Milnor-Wood type inequalities for Higgs bundles

Mathematics – Differential Geometry

Scientific paper

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Scientific paper

We explain how the generalized Milnor-Wood inequality of Burger and Iozzi for reductive representations of a cocompact complex-hyperbolic lattice into a Hermitian Lie group translates under Simpson's non-abelian Hodge correspondence into an inequality for topological invariants of the corresponding Higgs bundles. In this way, we obtain an inequality that holds for all Hermitian Lie groups, generalizing the Milnor-Wood type inequalities for Higgs bundles that have been proved for the classical Hermitian Lie groups by Bradlow, Garcia-Prada, and Gothen and by Koziarz and Maubon.

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