The norm of the Euler class

Article Article scientifique Article The norm of the Euler class eng 2012 author Bucher Michelle 737171 Section de mathématiques (MATH) Michelle Karlsson author Monod Nicolas 600377 523-544 10.1007/s00208-011-0694-8 0025-5831 http://link.springer.com/10.1007/s00208-011-0694-8 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. Dewey 510 25 Section de mathématiques 11 false Mathematische Annalen 353 2 27bc8006-4cd2-46a4-bfdf-041df40171a4 Article (Published version) Public Bucher-Monod2012_Article_TheNormOfTheEulerClass.pdf 288081 application/pdf openAccess Faculté des sciences / Section de mathématiques

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The norm of the Euler class	Mathematische Annalen			2012	442	242

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Bucher, Michelle