A characterization of higher rank symmetric spaces via bounded cohomology

Details A characterization of higher rank symmetric spaces via bounded cohomology A characterization of higher rank symmetric spaces via bounded cohomology

2007-02-09

arxiv.org/abs/math/0702274v3

Mathematics

Group Theory

Scientific paper

Let $M$ be complete nonpositively curved Riemannian manifold of finite volume whose fundamental group $\Gamma$ does not contain a finite index subgroup which is a product of infinite groups. We show that the universal cover $\tilde M$ is a higher rank symmetric space iff $H^2_b(M;\R)\to H^2(M;\R)$ is injective (and otherwise the kernel is infinite-dimensional). This is the converse of a theorem of Burger-Monod. The proof uses the celebrated Rank Rigidity Theorem, as well as a new construction of quasi-homomorphisms on groups that act on CAT(0) spaces and contain rank 1 elements.

Affiliated with

Also associated with

No associations

Rating

A characterization of higher rank symmetric spaces via bounded cohomology 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 A characterization of higher rank symmetric spaces via bounded cohomology, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A characterization of higher rank symmetric spaces via bounded cohomology will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-443790