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2012 Middle tunnels by splitting
Sangbum Cho, Darryl McCullough
Tohoku Math. J. (2) 64(4): 469-488 (2012). DOI: 10.2748/tmj/1356038975

Abstract

For a genus-1 1-bridge knot in $S^3$, 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.

Citation

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Sangbum Cho. Darryl McCullough. "Middle tunnels by splitting." Tohoku Math. J. (2) 64 (4) 469 - 488, 2012. https://doi.org/10.2748/tmj/1356038975

Information

Published: 2012
First available in Project Euclid: 20 December 2012

zbMATH: 1262.57010
MathSciNet: MR3008235
Digital Object Identifier: 10.2748/tmj/1356038975

Subjects:
Primary: 57M25

Keywords: (1,1), knot, torus knot, tunnel

Rights: Copyright © 2012 Tohoku University

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Vol.64 • No. 4 • 2012
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