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4:00 pm Thursday, April 21, 2011 Colloquium: Global Rigidity for certain actions of higher rank lattices on the torusby Federico Rodriguez Hertz (Penn State) in HB 227- In this talk we will give an approach to the following theorem: Let $\Gamma$ be an irreducible lattice in a connected semi-simple Lie group with finite center, no non-trivial compact factor and of rank bigger than one. Let $a:\Gamma \to Diff(T^N)$ be a real analytic action on the torus preserving an ergodic large measure (large means essentially that its support is non trivial in homotopy). $a$ induces a representation $a_0:\Gamma \to SL(N,Z)$. Assume further that $a_0$ has no zero weight and no rank one factor. Then $a$ and $a_0$ are conjugated by a real analytic map outside a finite $a_0$ invariant set. The theorem essentially says that nonlinear action $a$ is built from linear $a_0$ by blowing up finitely many point. This is joint work with A. Gorodnik, B. Kalinin and A. Katok.
Submitted by dani@rice.edu |