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SEMISIMPLE TUNNELS

Title
SEMISIMPLE TUNNELS
Author
조상범
Issue Date
2012-09
Publisher
PACIFIC JOURNAL MATHEMATICS
Citation
PACIFIC JOURNAL OF MATHEMATICS, v. 258, NO 1, Page. 51-89
Abstract
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.
URI
https://msp.org/pjm/2012/258-1/p03.xhtml
DOI
10.2140/pjm.2012.258.51
Appears in Collections:
COLLEGE OF EDUCATION[S](사범대학) > MATHEMATICS EDUCATION(수학교육과) > Articles
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