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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Presentation length and Simon’s conjecture
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by Ian Agol and Yi Liu PDF
J. Amer. Math. Soc. 25 (2012), 151-187 Request permission

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
  • MR Author ID: 671767
  • ORCID: 0000-0002-4254-8483
  • Email: ianagol@math.berkeley.edu
  • Yi Liu
  • Affiliation: Department of Mathematics, University of California, Berkeley, 970 Evans Hall #3840, Berkeley, California 94720-3840
  • MR Author ID: 945775
  • Email: yliu@math.berkeley.edu
  • 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
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 25 (2012), 151-187
  • MSC (2010): Primary 57Mxx
  • DOI: https://doi.org/10.1090/S0894-0347-2011-00711-X
  • MathSciNet review: 2833481