An infinite family of non-Haken hyperbolic 3-manifolds with vanishing Whitehead groups

A manifold M is said to be aspherical if its universal covering space is contractible. Farrell and Hsiang have conjectured [3]: Conjecture A. (Topological rigidity of aspherical manifolds.) Any homotopy equivalence f: N → M between closed aspherical manifolds is homotopic to a homeomorphism, and its analogue in algebraic K -theory: Conjecture B . The Whitehead groups Wh j (π 1 M)(j ≥ 0) of the fundamental group of a closed aspherical manifold M vanish.