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

References in corpus (5)

• Epimorphisms between 2-bridge link groups
• Twisted Alexander polynomials and a partial order on the set of prime knots
• Simon's conjecture for 2-bridge knots
• Knot Group Epimorphisms, II
• A partial order on the set of prime knots with up to 11 crossings

Cited by in corpus (2)

• Small optimal Margulis numbers force upper volume bounds
• Upper bounds in the Ohtsuki-Riley-Sakuma partial order on 2-bridge knots