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research article
The norm of the Euler class
We prove that the norm of the Euler class $\mathcal{E}$ for flat vector bundles is $2^{-n}$ (in even dimension $n$, since it vanishes in odd dimension). This shows that the Sullivan-Smillie bound considered by Gromov and Ivanov-Turaev is sharp. We construct a new cocycle representing $\mathcal{E}$ and taking only the two values $\pm 2^{-n}$; a null-set obstruction prevents any cocycle from existing on the projective space. We establish the uniqueness of an antisymmetric representative for $\mathcal{E}$ in bounded cohomology.
Type
research article
Web of Science ID
WOS:000303869200013
Authors
Publication date
2012
Publisher
Published in
Volume
353
Issue
2
Start page
523
End page
544
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
September 15, 2010
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