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- W4367181100 abstract "Abstract Let $alpha $ be a $C^{infty }$ volume-preserving action on a closed n -manifold M by a lattice $Gamma $ in $mathrm {SL}(n,mathbb {R})$ , $nge 3$ . Assume that there is an element $gamma in Gamma $ such that $alpha (gamma )$ admits a dominated splitting. We prove that the manifold M is diffeomorphic to the torus ${{mathbb T}^{n}={mathbb R}^{n}/{mathbb Z}^{n}}$ and $alpha $ is smoothly conjugate to an affine action. Anosov diffeomorphisms and partial hyperbolic diffeomorphisms admit a dominated splitting. We obtained a topological global rigidity when $alpha $ is $C^{1}$ . We also prove similar theorems for actions on $2n$ -manifolds by lattices in $textrm {Sp}(2n,{mathbb R})$ with $nge 2$ and $mathrm {SO}(n,n)$ with $nge 5$ ." @default.
- W4367181100 created "2023-04-28" @default.
- W4367181100 creator A5065906926 @default.
- W4367181100 date "2023-04-27" @default.
- W4367181100 modified "2023-09-28" @default.
- W4367181100 title "Global rigidity of higher rank lattice actions with dominated splitting" @default.
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- W4367181100 doi "https://doi.org/10.1017/etds.2023.31" @default.
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