On the growth rate of tunnel number of knots
| dc.creator | Kobayashi, Tsuyoshi | |
| dc.creator | Rieck, Yo'av | |
| dc.date | 2004-02-03 | |
| dc.date.accessioned | 2026-07-07T05:05:03Z | |
| dc.date.available | 2026-07-07T05:05:03Z | |
| dc.description | Given a knot $K$ in a closed orientable manifold $M$ we define the growth rate of the tunnel number of $K$ to be $gr_t(K) = \limsup_{n \to \infty} \frac{t(nK) - n t(K)}{n-1}$. 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 $S^3$ is never asymptotically super additive. The main result gives conditions that imply falsehood of Morimoto's Conjecture. | |
| dc.description | 19 pages, 8 figures | |
| dc.identifier | https://arxiv.org/abs/math/0402025 | |
| dc.identifier | http://arxiv.org/abs/math/0402025 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70039 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M99 | |
| dc.title | On the growth rate of tunnel number of knots | |
| dc.type | text |