Bounded cohomology, Higgs bundles, and Milnor-Wood inequalities

Abstract

We explain how the generalized Milnor-Wood inequality for reductive representations of a cocompact complex-hyperbolic lattice into a Hermitian Lie group translates, under the non-abelian Hodge correspondence, into various kinds of Milnor-Wood inequalities for Higgs bundles. This clarifies the relation between the representation theoretic generalized Milnor-Wood inequality and the various different versions of Milnor-Wood inequalities for Higgs bundles that are known in the literature.

Revised version

References in corpus (1)

• Maximal surface group representations in isometry groups of classical Hermitian symmetric spaces

Cited by in corpus (1)

• Model Higgs bundles in exceptional components of the $\text{Sp(4}\text{,}\mathbb{R}\text{)}$-character variety