Anosov representations: Domains of discontinuity and applications

Details Anosov representations: Domains of discontinuity and applications Anosov representations: Domains of discontinuity and applications

2011-08-03

arxiv.org/abs/1108.0733v2

Mathematics

Differential Geometry

63 pages, accepted for publication in Inventiones Mathematicae

Scientific paper

The notion of Anosov representations has been introduced by Labourie in his study of the Hitchin component for SL(n,R). Subsequently, Anosov representations have been studied mainly for surface groups, in particular in the context of higher Teichmueller spaces, and for lattices in SO(1,n). In this article we extend the notion of Anosov representations to representations of arbitrary word hyperbolic groups and start the systematic study of their geometric properties. In particular, given an Anosov representation of $\Gamma$ into G we explicitly construct open subsets of compact G-spaces, on which $\Gamma$ acts properly discontinuously and with compact quotient. As a consequence we show that higher Teichmueller spaces parametrize locally homogeneous geometric structures on compact manifolds. We also obtain applications regarding (non-standard) compact Clifford-Klein forms and compactifications of locally symmetric spaces of infinite volume.

Affiliated with

Also associated with

No associations

Rating

Anosov representations: Domains of discontinuity and applications 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 Anosov representations: Domains of discontinuity and applications, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Anosov representations: Domains of discontinuity and applications will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-663360