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

Title & Authors
ON THE 2-BRIDGE KNOTS OF DUNWOODY (1, 1)-KNOTS
Kim, Soo-Hwan; Kim, Yang-Kok;

Abstract
Every (1, 1)-knot is represented by a 4-tuple of integers (a, b, c, r), where a > 0, b $\small{\geq}$ 0, c $\small{\geq}$ 0, d = 2a+b+c, $\small{r\;{\in}\;\mathbb{Z}_d}$, 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;
Language
English
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