Middle tunnels by splitting

Details Middle tunnels by splitting Middle tunnels by splitting

2011-08-17

arxiv.org/abs/1108.3425v1

Mathematics

Geometric Topology

20 pages, 11 figures

Scientific paper

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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