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Iterated splitting and the classification of knot tunnels

Title
Iterated splitting and the classification of knot tunnels
Author
조상범
Keywords
knot; tunnel; (1,1); torus knot; regular; splitting; 2-bridge
Issue Date
2013-04
Publisher
Math SOC Japan
Citation
Journal of the Mathematical Society of Japan, 2013, 65(2), P.671-686
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. In a previous paper, we generalized their construction and calculated the slope invariants for the resulting examples. We give an iterated version of the construction that produces many more examples, and calculate their slope invariants. If one starts with the trivial knot, the iterated constructions produce all the 2-bridge knots, giving a new calculation of the slope invariants of their tunnels. In the final section we compile a list of the known possibilities for the set of tunnels of a given tunnel number 1 knot.
URI
https://projecteuclid.org/euclid.jmsj/1366896647http://hdl.handle.net/20.500.11754/52896
ISSN
0025-5645; 1881-1167
DOI
10.2969/jmsj/06520671
Appears in Collections:
COLLEGE OF EDUCATION[S](사범대학) > MATHEMATICS EDUCATION(수학교육과) > Articles
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