TY - JOUR
AU - 조상범
DA - 2013/04
PY - 2013
UR - https://projecteuclid.org/euclid.jmsj/1366896647
UR - http://hdl.handle.net/20.500.11754/52896
AB - 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.
PB - Math SOC Japan
KW - knot
KW - tunnel
KW - (1,1)
KW - torus knot
KW - regular
KW - splitting
KW - 2-bridge
TI - Iterated splitting and the classification of knot tunnels
IS - 2
VL - 65
DO - 10.2969/jmsj/06520671
T2 - JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN
ER -