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.


Published in:
Mathematische Annalen, 353, 2, 523-544
Year:
2012
Publisher:
Springer Verlag
ISSN:
0025-5831
Keywords:
Laboratories:




 Record created 2010-09-15, last modified 2018-01-28


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