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

Abstract

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