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- W2963995747 abstract "In this article we prove global rigidity results for hyperbolic actions of higher-rank lattices. Suppose $Gamma$ is a lattice in semisimple Lie group, all of whose factors have rank $2$ or higher. Let $alpha$ be a smooth $Gamma$-action on a compact nilmanifold $M$ that lifts to an action on the universal cover. If the linear data $rho$ of $alpha$ contains a hyperbolic element, then there is a continuous semiconjugacy intertwining the actions of $alpha$ and $rho$, on a finite-index subgroup of $Gamma$. If $alpha$ is a $C^infty$ action and contains an Anosov element, then the semiconjugacy is a $C^infty$ conjugacy. As a corollary, we obtain $C^infty$ global rigidity for Anosov actions by cocompact lattices in semisimple Lie group with all factors rank $2$ or higher. We also obtain global rigidity of Anosov actions of $mathrm{SL}(n,mathbb Z)$ on $mathbb T^n$ for $ ngeq 5$ and probability-preserving Anosov actions of arbitrary higher-rank lattices on nilmanifolds." @default.
- W2963995747 created "2019-07-30" @default.
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- W2963995747 date "2017-11-01" @default.
- W2963995747 modified "2023-10-03" @default.
- W2963995747 title "Global smooth and topological rigidity of hyperbolic lattice actions" @default.
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- W2963995747 doi "https://doi.org/10.4007/annals.2017.186.3.3" @default.
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