The norm of the Euler class

Details The norm of the Euler class The norm of the Euler class

2010-09-13

arxiv.org/abs/1009.2316v1

Mathematics

Geometric Topology

19 pages

Scientific paper

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. We construct a new cocycle representing 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 E in bounded cohomology.

Affiliated with

Also associated with

No associations

Rating

The norm of the Euler class does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The norm of the Euler class, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The norm of the Euler class will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-337260