Surjectivity of the comparison map in bounded cohomology for hermitian Lie groups
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 sem...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
Apr 2012
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| In: |
International mathematics research notices
Year: 2012, Issue: 9, Pages: 2068-2093 |
| ISSN: | 1687-0247 |
| Online Access: | Verlag, Volltext: http://www.redi-bw.de/db/ebsco.php/search.ebscohost.com/login.aspx%3fdirect%3dtrue%26db%3da9h%26AN%3d75054830%26site%3dehost-live
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| Author Notes: | Tobias Hartnick and Andreas Ott |
MARC
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| 520 | |a 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. | ||
| 650 | 4 | |a Characteristic classes | |
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