Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

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

Andrew J. Nicasa1

a1 Department of Mathematics, University of Toronto, Toronto M5S 1A1, Canada

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 Whj1M)(j ≥ 0) of the fundamental group of a closed aspherical manifold M vanish.

(Received March 13 1985)