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

Kim, Soo-Hwan;Kim, Yang-Kok

• Received : 2009.06.22
• Published : 2011.01.31
• 26 4

#### 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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#### Acknowledgement

Supported by : Dong-eui University