An introduction to Anosov representations
Student No.:50
Time:Tue/Thu 13:00-14:50, 2017-07-04~2017-07-27
Instructor:Tengren Zhang  [California Institute of Technology]
Place:Conference Room 4, floor 2, Jin Chun Yuan West Building
Starting Date:2017-7-4
Ending Date:2017-7-27

The class on July 25 has been canceled.






I will give an introduction to the theory of Anosov representations. These are a particular class of representations from hyperbolic groups to reductive Lie groups that have ``good geometric properties”. One should think of the Anosov property as a generalization of the notion of convex cocompactness in the setting of rank 1 Lie groups to higher rank Lie groups. There will be a focus on examples, which include Hitchin representations, maximal representations, and holonomies of convex real projectice structures on closed hyperbolic manifolds.







Some basic Lie theory, hyperbolic geometry, and theory of smooth manifolds. Understanding the notion of (G,X)-structures will help, but is not required.







F. Labourie; Anosov flows, Surface Groups and Curves in Projective Space; Inventiones Mathematicae 165(1) (2006), pp 51-114.


O. Guichard, Anna Wienhard; Anosov representations: domains of discontinuity and applications; Inventiones Mathematicae 190(2) (2012), pp 357-438.


M. Kapovich, B. Leeb, J. Porti; Morse actions on discrete groups on symmetric spaces, arXiv:143.7671


F. Gueritaud, O. Guichard, F. Kassel, A. Wienhard; Anosov representations and proper actions; Geometry and Topology 21 (2017), pp 485-584.