If is a lattice, we define an invariant of a representation using the Borel class . We show that this invariant satisfies a Milnor–Wood type inequality and its maximal value is attained precisely by the representations conjugate to the restriction to of the irreducible complex -dimensional representation of or its complex conjugate. Major ingredients of independent interest are the study of our extension to degenerate configurations of flags of a cocycle defined by Goncharov, as well as the identification of as a normed space.
"The bounded Borel class and -manifold groups." Duke Math. J. 167 (17) 3129 - 3169, 15 November 2018. https://doi.org/10.1215/00127094-2018-0038