38 research outputs found
Convex cocompact actions in real projective geometry
We study a notion of convex cocompactness for (not necessarily irreducible)
discrete subgroups of the projective general linear group acting on real
projective space, and give various characterizations. A convex cocompact group
in this sense need not be word hyperbolic, but we show that it still has some
of the good properties of classical convex cocompact subgroups in rank-one Lie
groups. Extending our earlier work arXiv:1701.09136 from the context of
projective orthogonal groups, we show that for word hyperbolic groups
preserving a properly convex open set in projective space, the above general
notion of convex cocompactness is equivalent to a stronger convex cocompactness
condition studied by Crampon-Marquis, and also to the condition that the
natural inclusion be a projective Anosov representation. We investigate
examples.Comment: 77 pages, 6 figures. Added appendix. Removed section on Anosov
right-angled reflection groups, which will appear as a separate pape
Anosov representations and proper actions
We establish several characterizations of Anosov representations of word
hyperbolic groups into real reductive Lie groups, in terms of a Cartan
projection or Lyapunov projection of the Lie group. Using a properness
criterion of Benoist and Kobayashi, we derive applications to proper actions on
homogeneous spaces of reductive groups.Comment: 73 pages, 4 figures; to appear in Geometry & Topolog