About some infinite family of 2-bridge knots and 3-manifolds

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 (ℓ+1)2 or (ℓ+1)1, that are the closure of the rational (2ℓ−1)/(ℓ−1)-tangles or (2ℓ−1)/ℓ-tangles, respectively.