Tsuyoshi Kobayashi, Yoav Rieck
On the growth rate of the tunnel number of knots
Given a knot K in a closed orientable manifold M we define the growth rate of the tunnel number of K to be . As our main result we prove that the Heegaard genus of M is strictly less than the Heegaard genus of the knot exterior if and only if the growth rate is less than 1. In particular this shows that a non-trivial knot in S3 is never asymptotically super additive. The main result gives conditions that imply falsehood of Morimoto's Conjecture.
Journal fur die reine und angewandte Mathematik (Crelles Journal), Walter de Gruyter
Print ISSN: 0075-4102
Volume: 2006, 03/2006
Pages: 63 - 78
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