Presentation length and Simon's conjecture

Details Presentation length and Simon's conjecture Presentation length and Simon's conjecture

2010-06-28

arxiv.org/abs/1006.5262v3

Mathematics

Geometric Topology

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

Scientific paper

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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