TY - JOUR
AU - 조상범
DA - 2012/09
PY - 2012
UR - https://msp.org/pjm/2012/258-1/p03.xhtml
AB - A knot in S-3 in genus-1 1-bridge position (called a (1, 1)-position) can be described by an element of the braid group of two points in the torus. Our main results tell how to translate between a braid group element and the sequence of slope invariants of the upper and lower tunnels of the (1, 1)-position. After using them to verify previous calculations of the slope invariants for all tunnels of 2-bridge knots and (1, 1)-tunnels of torus knots, we obtain characterizations of the slope sequences of tunnels of 2-bridge knots, and of a class of tunnels we call toroidal. The main results lead to a general algorithm to calculate the slope invariants of the upper and lower tunnels from a braid description. The algorithm has been implemented as software, and we give some sample computations.
PB - PACIFIC JOURNAL MATHEMATICS
TI - SEMISIMPLE TUNNELS
IS - 1
VL - 258
DO - 10.2140/pjm.2012.258.51
T2 - PACIFIC JOURNAL OF MATHEMATICS
ER -