On the degeneration of tunnel numbers under connected sum

Tao Li; Ruifeng Qiu

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arXiv · 1310.5054

On the degeneration of tunnel numbers under connected sum

Tao Li·Ruifeng Qiu

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Abstract

We show that, for any integer $n\ge 3$, there is a prime knot $k$ such that (1) $k$ is not meridionally primitive, and (2) for every $m$-bridge knot $k'$ with $m\leq n$, the tunnel numbers satisfy $t(k\# k')\le t(k)$. This gives counterexamples to a conjecture of Morimoto and Moriah on tunnel number under connected sum and meridionally primitive knots.

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BibTeX RIS

Tao Li, Ruifeng Qiu. 2013-10-22. On the degeneration of tunnel numbers under connected sum. https://arxiv.org/abs/1310.5054

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