On the growth rate of tunnel number of knots

Tsuyoshi Kobayashi, Yo'av Rieck

Given a knot $K$ in a closed orientable manifold $M$ we define the growth rate of the tunnel number of $K$ to be $g{r}_t(K)={\mathrm{limsup}}_{n\to \infty }\frac{t(nK)-nt(K)}{n-1}$. As o…