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- Title
Surjectivity of the Comparison Map in Bounded Cohomology for Hermitian Lie Groups.
- Authors
Hartnick, Tobias; Ott, Andreas
- Abstract
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.
- Subjects
OPERATIONS (Algebraic topology); DIFFERENTIAL equations; CHARACTERISTIC classes; LIE groups; DIFFERENTIAL topology
- Publication
IMRN: International Mathematics Research Notices, 2012, Vol 2012, Issue 9, p2068
- ISSN
1073-7928
- Publication type
Article