3-manifold groups and property $T$ of Kazhdan

Abstract

Suppose that $M$ is a compact, orientable three-manifold such that each piece of the canonical decomposition along embedded spheres, discs and tori admits one of the eight geometric structures of three-manifolds in the sense of Thurston. Let $G$ be a subgroup of $\pi_1(M)$. If $G$ has property $T$ in the sense of Kazhdan, then $G$ is finite.