The property $(T_n)_{L^1}$ Zimmer conjecture

Let $\Gamma$ be a group with property $(T_n)_{L^1}$, meaning the $L^1$-coefficient form of higher property T used in the source. The $(T_n)_{L^1}$ Zimmer conjecture. Every diffeomorphic action of $\Gamma$ on a compact manifold of dimension at most $n$ factors through a finite quotient. This is presented as an extension of Zimmer's conjecture beyond lattices; the source gives no resolution status.