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On the growth rate of the tunnel number of knots
-
Tsuyoshi Kobayashi
and
Yo’av Rieck
Published/Copyright:
May 4, 2006
Abstract
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.
Received: 2004-06-22
Accepted: 2005-01-24
Published Online: 2006-05-04
Published in Print: 2006-03-24
© Walter de Gruyter
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- On the growth rate of the tunnel number of knots
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Articles in the same Issue
- Lines on projective hypersurfaces
- Almost isomorphism for countable state Markov shifts
- Inhomogeneous and Euclidean spectra of number fields with unit rank strictly greater than 1
- On the growth rate of the tunnel number of knots
- Signature homology
- On the structure of cofree Hopf algebras
- Exponential product approximation to the integral kernel of the Schrödinger semigroup and to the heat kernel of the Dirichlet Laplacian
- κ-types and Γ-asymptotic expansions
