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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Presentation length and Simon's conjecture


Authors: Ian Agol and Yi Liu
Journal: J. Amer. Math. Soc. 25 (2012), 151-187
MSC (2010): Primary 57Mxx
Published electronically: July 12, 2011
MathSciNet review: 2833481
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Abstract: In this paper, we show that any knot group maps onto at most finitely many knot groups. This gives an affirmative answer to a conjecture of J. Simon. We also bound the diameter of a closed hyperbolic 3-manifold linearly in terms of the presentation length of its fundamental group, improving a result of White.


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Additional Information

Ian Agol
Affiliation: Department of Mathematics, University of California, Berkeley, 970 Evans Hall #3840, Berkeley, California 94720-3840
Email: ianagol@math.berkeley.edu

Yi Liu
Affiliation: Department of Mathematics, University of California, Berkeley, 970 Evans Hall #3840, Berkeley, California 94720-3840
Email: yliu@math.berkeley.edu

DOI: http://dx.doi.org/10.1090/S0894-0347-2011-00711-X
PII: S 0894-0347(2011)00711-X
Received by editor(s): July 12, 2010
Received by editor(s) in revised form: April 22, 2011
Published electronically: July 12, 2011
Additional Notes: The first and second authors were partially supported by NSF grant DMS-0806027
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.