Three proofs from dynamics of rigidity of surface group actions

In previous talks (not a prerequisite!), I've described examples of actions of a surface group G on the circle that are totally rigid -- they are essentially isolated points in the representation space Hom(G, Homeo+(S^1))/~.   These examples are interesting from many perspectives, ranging from foliation theory to the classification of connected components of representation spaces.    

In this talk, I will illustrate three separate approaches to prove rigidity of these actions, including my original proof.   Each one uses fundamentally different techniques, but all have a common dynamical flavor:

1. Structural stability of Anosov foliations (Ghys/Bowden, under extra hypotheses)

2. Rotation number "trace coordinates" on the representation space (Mann)

3. New "ping-pong" lemmas for surface groups (Matsumoto)

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