Abstract
A theorem of Tits and Vinberg allows to build an action of a Coxeter group \Gamma on a properly convex open set \Omega of the real projective space, thanks to the data P of a polytope and reflection across its facets. We give sufficient conditions for such action to be of finite covolume, convex-cocompact or geometrically finite. We describe a hypothesis that makes those conditions necessary. Under this hypothesis, we describe the Zariski closure of \Gamma , nd the maximal \Gamma -invariant convex set, when there is a unique \Gamma -invariant convex set, when the convex set \Omega is strictly convex, when we can find a \Gamma -invariant convex set \Omega ' which is strictly convex.
Submitted Version (
Free)
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call