Mathematische Annalen

, Volume 353, Issue 2, pp 523–544 | Cite as

The norm of the Euler class



We prove that the norm of the Euler class \({\mathcal {E}}\) for flat vector bundles is 2n (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. In the course of the proof, we construct a new cocycle representing \({\mathcal {E}}\) and taking only the two values ±2n. Furthermore, we establish the uniqueness of a canonical bounded Euler class.

Mathematics Subject Classification (1991)

57R20 22E41 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Université de GenèveGenevaSwitzerland
  2. 2.EPFLLausanneSwitzerland

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