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Whitehead groups of certain hyperbolic manifolds

Published online by Cambridge University Press:  24 October 2008

A. J. Nicas  and
C. W. Stark
A. J. Nicas
Affiliation:
University of Toronto
C. W. Stark
Affiliation:
Brandeis University
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Extract

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 π1M, 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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 95 , Issue 2 , March 1984 , pp. 299 - 308
Copyright
Copyright © Cambridge Philosophical Society 1984

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References

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