Zimmer's conjecture: Subexponential growth, measure rigidity, and strong property (T)
Zimmer's conjecture: Subexponential growth, measure rigidity, and strong property (T)
We prove several cases of Zimmer's conjecture for actions of higher-rank, cocompact lattices on low-dimensional manifolds. For example, if $\Gamma$ is a cocompact lattice in $\mathrm{SL}(n, \mathbb{R})$, $M$ is a compact manifold, and $\omega$ a volume form on $M$, we show that any homomorphism $\alpha\colon \Gamma \rightarrow \mathrm{Diff}(M)$ has finite …