Vol3 and other exceptional hyperbolic 3-manifolds

Authors:
K. N. Jones and A. W. Reid

Journal:
Proc. Amer. Math. Soc. **129** (2001), 2175-2185

MSC (2000):
Primary 57M50

Published electronically:
December 4, 2000

MathSciNet review:
1825931

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Abstract | References | Similar Articles | Additional Information

Abstract: D. Gabai, R. Meyerhoff and N. Thurston identified seven families of exceptional hyperbolic manifolds in their proof that a manifold which is homotopy equivalent to a hyperbolic manifold is hyperbolic. These families are each conjectured to consist of a single manifold. In fact, an important point in their argument depends on this conjecture holding for one particular exceptional family. In this paper, we prove the conjecture for that particular family, showing that the manifold known as in the literature covers no other manifold. We also indicate techniques likely to prove this conjecture for five of the other six families.

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Additional Information

**K. N. Jones**

Affiliation:
Department of Mathematical Sciences, Ball State University, Muncie, Indiana 47304

Email:
kerryj@math.bsu.edu

**A. W. Reid**

Affiliation:
Department of Mathematics, University of Texas, Austin, Texas 78712

Email:
areid@math.utexas.edu

DOI:
http://dx.doi.org/10.1090/S0002-9939-00-05775-0

Keywords:
Hyperbolic 3-manifold,
arithmetic manifold,
homotopy hyperbolic 3-manifold

Received by editor(s):
April 19, 1999

Received by editor(s) in revised form:
October 13, 1999, and November 8, 1999

Published electronically:
December 4, 2000

Additional Notes:
The first author was partially supported by Ball State University.

The second author was partially supported by the Royal Society, NSF, the A. P. Sloan Foundation and a grant from the Texas Advanced Research Program.

Communicated by:
Ronald A. Fintushel

Article copyright:
© Copyright 2000
American Mathematical Society