Vol3 and other exceptional hyperbolic 3-manifolds
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- by K. N. Jones and A. W. Reid PDF
- Proc. Amer. Math. Soc. 129 (2001), 2175-2185 Request permission
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 $\mathrm {Vol}3$ in the literature covers no other manifold. We also indicate techniques likely to prove this conjecture for five of the other six families.References
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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
- MR Author ID: 146355
- Email: areid@math.utexas.edu
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 2175-2185
- MSC (2000): Primary 57M50
- DOI: https://doi.org/10.1090/S0002-9939-00-05775-0
- MathSciNet review: 1825931