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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Volumes of hyperbolic Haken manifolds, II


Authors: Marc Culler and Peter B. Shalen
Journal: Proc. Amer. Math. Soc. 125 (1997), 3059-3067
MSC (1991): Primary 57M50; Secondary 57N10
MathSciNet review: 1422858
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Abstract: We show that if $M$ is a closed hyperbolic 3-manifold and if $\pi _{1}(M)$ has a non-abelian free quotient, then the volume of $M$ is greater than $0.92$. If, in addition, $\pi _{1}(M)$ contains no genus-$2$ surface groups, then the volume of $M$ is greater than $1.02$. Using these results we show that if there are infinitely many primitive homology classes in $H_{2}(M;\mathbb {Z})$ which are not represented by fibroids, then the volume of $M$ is greater than $0.83$.


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Additional Information

Marc Culler
Affiliation: Department of Mathematics (M/C 249), University of Illinois at Chicago, 851 S. Morgan St., Chicago, Illinois 60607-7045

Peter B. Shalen
Affiliation: Department of Mathematics (M/C 249), University of Illinois at Chicago, 851 S. Morgan St., Chicago, Illinois 60607-7045
Email: culler@math.uic.edu, shalen@math.uic.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-97-04101-4
PII: S 0002-9939(97)04101-4
Received by editor(s): November 6, 1995
Additional Notes: This research was partially supported by National Science Foundation grant DMS9302520.
Communicated by: James West
Article copyright: © Copyright 1997 American Mathematical Society