Anosov representations were introduced by Labourie for fundamental groups of closed negatively curved Riemannian manifolds in his study of the Hitchin component and further generalized by Guichard-Wienhard for more general Gromov hyperbolic groups. Anosov representations of hyperbolic groups form a rich and structurally stable class of discrete subgroups of real reductive Lie groups and are recognized as a higher rank analogue of classical convex cocompact representations of word hyperbolic groups into simple Lie groups of real rank 1. In this thesis, we obtain characterizations of Anosov representations in the spirit of the work of Gu\'eritaud-Guichard-Kassel-Wienhard and Kapovich-Leeb-Porti in terms of equivariant limit maps, the Cartan property, the uniform gap summation property and weak uniform eigenvalue gaps. As an application, we obtain a characterization of strongly convex cocompact subgroups of the projective linear group PGL(d,R). We also compute the Holder exponent of the Anosov limit maps of an Anosov representation in terms of the Cartan and Lyapunov projection of the image of the representation. Finally, we also provide a complete characterization of the domain groups of Borel Anosov representations into the projective linear group PGL(4q+2,R) for every q \geq 1.

Kostas' advisor is Dick Canary.

Zoom:
https://umich.zoom.us/j/2438829474
Passcode: seLR31

Speaker(s): Konstantinos Tsouvalas (UM)