On the Cyclic Branched Coverings of the 2-Bridge Knot b(17,4)

Abstract

We construct an infinite family of hyperbolic 3-manifolds whose fundamental groups are cyclically presented. We prove that these 3-manifolds are cyclic branched coverings of S3over the 2-bridge knot b(17,4). Finally, we compute thehomology groups and discuss the spines of our manifolds which correspond to some group presentations.