Presentation length and Simon's conjecture

2010/06/28 by Ian Agol, Yi Liu, Agol, Ian +1
Mathematics · #57M #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M

paper · pdf · doi:10.48550/arxiv.1006.5262

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

arxiv created 2011/05/17 · arxiv updated 2011/05/19

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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