조상범
2018-03-27T02:09:34Z
2018-03-27T02:09:34Z
2013-04
Journal of the Mathematical Society of Japan, 2013, 65(2), P.671-686
0025-5645
1881-1167
https://projecteuclid.org/euclid.jmsj/1366896647
http://hdl.handle.net/20.500.11754/52896
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.
The first author was supported by the research fund of Hanyang University (HY-2011-N).The second author was supported in part by NSF grant DMS-0802424.
en
Math SOC Japan
knot
tunnel
(1,1)
torus knot
regular
splitting
2-bridge
Iterated splitting and the classification of knot tunnels
Article
2
65
10.2969/jmsj/06520671
671-686
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN
Cho, Sangbum
McCullough, Darryl
2013011057
S
COLLEGE OF EDUCATION[S]
DEPARTMENT OF MATHEMATICS EDUCATION
scho