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Vol3 and other exceptional hyperbolic 3-manifolds
Author(s):
K.
N.
Jones;
A.
W.
Reid
Journal:
Proc. Amer. Math. Soc.
129
(2001),
2175-2185.
MSC (2000):
Primary 57M50
Posted:
December 4, 2000
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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:
10.1090/S0002-9939-00-05775-0
PII:
S 0002-9939(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
Posted:
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
Copyright of article:
Copyright
2000,
American Mathematical Society
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