Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Whitehead groups of certain hyperbolic manifolds

A. J. Nicasa1 and C. W. Starka2

a1 University of Toronto

a2 Brandeis University

An aspherical manifold is a connected manifold whose universal cover is contractible. It has been conjectured that the Whitehead groups Whj (π1 M) (including the projective class group, the original Whitehead group of π1 M, and the higher Whitehead groups of [9]) vanish for any compact aspherical manifold M. The present paper considers this conjecture for twelve hyperbolic 3-manifolds constructed from regular hyperbolic polyhedra. Hyperbolic manifolds are of special interest in this regard since so much is known about their topology and geometry and very little is known about the algebraic K-theory of hyperbolic manifolds whose fundamental groups are not generalized free products.

(Received September 14 1983)