Presentation length and Simon's conjecture

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.

34 pages, 3 figures, fixed some errors, especially in the proof of Prop. 7.2. Final version to appear in Journal of the American Mathematical Society