Surjectivity of the comparison map in bounded cohomology for hermitian Lie groups - Hartnick, Tobias; Ott, Andreas (International mathematics research notices, 2012)
We investigate the implications of Gromov’s theorem on boundedness of primary characteristic classes for the continuous bounded cohomology of a semisimple Lie group G. We deduce that the comparison map from continuous bounded cohomology to continuous cohomology is surjective for a large class of semisimple Lie groups, including all Hermitian groups. Our proof is based on a geometric implementation of the canonical map from the cohomology of the classifying space of G to the continuous group cohomology of G. We obtain this implementation by establishing a variant of Kobayashi-Ono-Hirzebruch duality.
Advance access publication June 3, 2011
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