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

Published online by Cambridge University Press:  24 October 2008

Andrew J. Nicas
Andrew J. Nicas
Affiliation:
Department of Mathematics, University of Toronto, Toronto M5S 1A1, Canada
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Extract

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 Whj(π1M)(j ≥ 0) of the fundamental group of a closed aspherical manifold M vanish.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 99 , Issue 2 , March 1986 , pp. 239 - 246
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

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