Anosov representations and proper actions
Dynamics on Moduli Spaces April 13, 2015 - April 17, 2015
Location: MSRI: Simons Auditorium
orthogonal and unitary groups of non-definite signature
37D20 - Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
37-XX - Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX]
20F65 - Geometric group theory [See also 05C25, 20E08, 57Mxx]
Anosov representations of word hyperbolic groups into reductive Lie groups provide a generalization of convex cocompact representations to higher real rank. I will explain how these representations can be used to construct properly discontinuous actions on homogeneous spaces. For a rank-one simple group G, this construction covers all proper actions on G, by left and right multiplication, of quasi-isometrically embedded discrete subgroups of G×G; in particular, such actions remain proper after small deformations, and we can describe them explicitly. This is joint work with F. Guéritaud, O. Guichard, and A. Wienhard.
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