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

Kim, Soo-Hwan;Kim, Yang-Kok

  • Received : 2009.06.22
  • Published : 2011.01.31

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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Cited by

  1. On the Polynomial of the Dunwoody (1, 1)-knots vol.52, pp.2, 2012, https://doi.org/10.5666/KMJ.2012.52.2.223
  2. Comparison and correlation of physical properties from the plain and slope sediments in the Ulleung Basin, East Sea (Sea of Japan) vol.19, pp.5, 2001, https://doi.org/10.1016/S1367-9120(00)00062-6
  3. Chirp (2–7 kHz) echo characters and geotechnical properties of surface sediments in the Ulleung Basin, the East Sea vol.3, pp.4, 1999, https://doi.org/10.1007/BF02910492
  4. The Dual and Mirror Images of the Dunwoody 3-Manifolds vol.2013, 2013, https://doi.org/10.1155/2013/103209

Acknowledgement

Supported by : Dong-eui University