Zimmer's conjecture for lattice actions: the $\mathrm{SL}(n,\mathbb{C})$-case

Abstract

We prove Zimmer's conjecture for co-compact lattices in $\mathrm{SL}(n,\mathbb{C})$: for any co-compact lattice in $\mathrm{SL}(n,\mathbb{C})$, $n\ge 3$, any $\Gamma$-action on a compact manifold $M$ with dimension: (I) less than $2n-2$ if $n\ne 4$, (II) less than $5$ if $n=4$, by $C^{1+\epsilon }$ diffeomorphisms factors through a finite action.

References in corpus (4)

• Groups acting on manifolds: around the Zimmer program
• Invariant measures and measurable projective factors for actions of higher-rank lattices on manifolds
• Euler characteristics and actions of automorphism groups of free groups
• Recent progress in the Zimmer program