Anosov representations and proper actions
Dynamics on Moduli Spaces April 13, 2015 - April 17, 2015
Location: SLMath: Eisenbud Auditorium
quotient manifolds
discrete subgroups
orthogonal and unitary groups of non-definite signature
Lorentz group
Cartan decomposition
proper actions
parabolic subgroup
35Q70 - PDEs in connection with mechanics of particles and systems of particles
35Q60 - PDEs in connection with optics and electromagnetic theory
20Jxx - Connections of group theory with homological algebra and category theory
14218
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.
Kassel.Notes
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