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The norm of the Euler class

Published inMathematische Annalen, vol. 353, no. 2, p. 523-544
Publication date2012
Abstract

We prove that the norm of the Euler class 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. In the course of the proof, we construct a new cocycle representing E and taking only the two values ±2−n . Furthermore, we establish the uniqueness of a canonical bounded Euler class.

Citation (ISO format)
BUCHER, Michelle, MONOD, Nicolas. The norm of the Euler class. In: Mathematische Annalen, 2012, vol. 353, n° 2, p. 523–544. doi: 10.1007/s00208-011-0694-8
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Additional URL for this publicationhttp://link.springer.com/10.1007/s00208-011-0694-8
Journal ISSN0025-5831
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