Middle tunnels by splitting

Sangbum Cho; Darryl McCullough

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arXiv · 1108.3425

Middle tunnels by splitting

Sangbum Cho·Darryl McCullough

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Abstract

For a genus-1 1-bridge knot in the 3-sphere, that is, a (1,1)-knot, a middle tunnel is a tunnel that is not an upper or lower tunnel for some (1,1)-position. Most torus knots have a middle tunnel, and non-torus-knot examples were obtained by Goda, Hayashi, and Ishihara. We generalize their construction and calculate the slope invariants for the resulting middle tunnels. In particular, we obtain the slope sequence of the original example of Goda, Hayashi, and Ishihara.

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Sangbum Cho, Darryl McCullough. 2011-08-17. Middle tunnels by splitting. https://arxiv.org/abs/1108.3425

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