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http://dx.doi.org/10.4134/BKMS.2011.48.1.197

ON THE 2-BRIDGE KNOTS OF DUNWOODY (1, 1)-KNOTS  

Kim, Soo-Hwan (DEPARTMENT OF MATHEMATICS DONG-EUI UNIVERSITY)
Kim, Yang-Kok (DEPARTMENT OF MATHEMATICS DONG-EUI UNIVERSITY)
Publication Information
Bulletin of the Korean Mathematical Society / v.48, no.1, 2011 , pp. 197-211 More about this Journal
Abstract
Every (1, 1)-knot is represented by a 4-tuple of integers (a, b, c, r), where a > 0, b $\geq$ 0, c $\geq$ 0, d = 2a+b+c, $r\;{\in}\;\mathbb{Z}_d$, and it is well known that all 2-bridge knots and torus knots are (1, 1)-knots. In this paper, we describe some conditions for 4-tuples which determine 2-bridge knots and determine all 4-tuples representing any given 2-bridge knot.
Keywords
(1,1)-knot; (1,1)-decomposition; cyclic branched covering; crystallization; Dunwoody manifold; Heegaard splitting; Heegaard diagram; 2-bridge knot; torus knot;
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