Abstract. Every (1, 1)-knot is represented by a 4-tuple of integers (a, b, c, r), where a > 0, b ≥ 0, c ≥ 0, d = 2a+ b + c, r ∈ 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.

Abstract. We construct an infinite family of 3-manifolds and show that these manifolds have cyclically presented fundamental groups and are cyclic branched coverings of the 3-sphere branched over the 2-bridge knots ( + 1) 2 or ( + 1) 1 , that are the closure of the rational (2 − 1)/( − 1)-tangles or (2 − 1)/ -tangles, respectively.