1 results
C1 actions on manifolds by lattices in Lie groups
- Part of
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- Journal:
- Compositio Mathematica / Volume 158 / Issue 3 / March 2022
- Published online by Cambridge University Press:
- 13 May 2022, pp. 529-549
- Print publication:
- March 2022
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- Article
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In this paper we study Zimmer's conjecture for
$C^{1}$ actions of lattice subgroup of a higher-rank simple Lie group with finite center on compact manifolds. We show that when the rank of an uniform lattice is larger than the dimension of the manifold, then the action factors through a finite group. For lattices in 
${\rm SL}(n, {{\mathbb {R}}})$, the dimensional bound is sharp.
