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Global rigidity results for lattice actions on tori and new examples of volume-preserving actions. (English) Zbl 0857.57038

Summary: Any action of a finite index subgroup in \(\text{SL} (n,\mathbb{Z})\), \(n\geq 4\) on the \(n\)-dimensional torus which has a finite orbit and contains an Anosov element which splits as a direct product is smoothly conjugate to an affine action. We also construct first examples of real-analytic volume-preserving actions of \(\text{SL} (n,\mathbb{Z})\) and other higher-rank lattices on compact manifolds which are not conjugate (even topologically) to algebraic models.

MSC:

57S25 Groups acting on specific manifolds
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