Presentation length and Simon’s conjecture

Agol, Ian; Liu, Yi

doi:10.1090/S0894-0347-2011-00711-X

Presentation length and Simon’s conjecture
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by Ian Agol and Yi Liu

J. Amer. Math. Soc. 25 (2012), 151-187

DOI: https://doi.org/10.1090/S0894-0347-2011-00711-X

Published electronically: July 12, 2011

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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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