2009/05/20 by Tobias Hartnick, Hartnick, Tobias, Andreas Ott +1
Mathematics · #22E41 #53C35 #55N35 #57T15 #Advanced Algebra and Geometry #Algebraic Topology (math.AT) #FOS: Mathematics #Geometry and complex manifolds #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.AT #math.GR #msc:22E41 #msc:53C35 #msc:55N35 #msc:57T15
paper · pdf · doi:10.48550/arxiv.0905.3395
Streamlined exposition, minor errors corrected; 19 pages
openalex publication_date 2009/05/20 · arxiv created 2009/12/01 · arxiv updated 2009/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove surjectivity of the comparison map from continuous bounded cohomology to continuous cohomology for Hermitian Lie groups with finite center. For general semisimple Lie groups with finite center, the same argument shows that the image of the comparison map contains all the even generators. Our proof uses a Hirzebruch type proportionality principle in combination with Gromov's results on boundedness of primary characteristic classes and classical results of Cartan and Borel on the cohomology of compact homogeneous spaces.