## Smooth Factors of Projective Actions of Higher Rank Lattices and Rigidity

#### Ralf SpatzierUniversity of Michigan

This is joint work with Alex Gorodnik. We study smooth factors of projective action of higher rank lattices $\Gamma$ in a semsimple group $G$ on $G/P$, $P$ a parabolic. Under a mild condition on existence of a differentiable sink, we show that these actions are $C^{\infty}$ conjugate to a projective action.

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