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The volume of a closed hyperbolic 3-manifold is bounded by $\pi$ times the length of any presentation of its fundamental group

Author(s): Daryl Cooper
Journal: Proc. Amer. Math. Soc. 127 (1999), 941-942.
MSC (1991): Primary 30F40, 57M50
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References:

1.
I. Chavel. Riemannian Geometry: A Modern Introduction. Cambridge University Press (1993). MR 95j:53001
2.
M. White. UCSB Thesis, to appear.

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Additional Information:

Daryl Cooper
Affiliation: Department of Mathematics, University of California at Santa Barbara, Santa Barbara, California 93106-0001
Email: cooper@math.ucsb.edu

DOI: 10.1090/S0002-9939-99-05190-4
PII: S 0002-9939(99)05190-4
Received by editor(s): August 3, 1998
Additional Notes: The author's research was supported in part by the NSF
Communicated by: Ronald A. Fintushel
Copyright of article: Copyright 1999, American Mathematical Society

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