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SEMISIMPLE TUNNELS
- Authors
- Cho, Sangbum; Mccullough, Darryl
- Issue Date
- Jul-2012
- Publisher
- University of California at Berkeley
- Keywords
- knot; tunnel; (1,1); braid; torus; slope; invariant; cabling; semisimple; 2-bridge; toroidal; algorithm
- Citation
- Pacific Journal of Mathematics, v.258, no.1, pp 51 - 89
- Pages
- 39
- Indexed
- SCIE
SCOPUS
- Journal Title
- Pacific Journal of Mathematics
- Volume
- 258
- Number
- 1
- Start Page
- 51
- End Page
- 89
- ISSN
- 0030-8730
- 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.
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Collections - 서울 사범대학 > 서울 수학교육과 > 1. Journal Articles
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Related Researcher
- Cho, Sang bum
- COLLEGE OF EDUCATION (DEPARTMENT OF MATHEMATICS EDUCATION)