The spectrum of the growth rate of the tunnel number is infinite

Baker, Kenneth; Kobayashi, Tsuyoshi; Rieck, Yo’av

doi:10.1090/proc/12957

The spectrum of the growth rate of the tunnel number is infinite
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by Kenneth L. Baker, Tsuyoshi Kobayashi and Yo’av Rieck PDF

Proc. Amer. Math. Soc. 144 (2016), 3609-3618 Request permission

Abstract:

For any $\epsilon > 0$ we construct a hyperbolic knot $K \subset S^{3}$ for which $1 - \epsilon < \mathrm {gr}_t(K) < 1$. This shows that the spectrum of the growth rate of the tunnel number is infinite.

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