On three-fold irregular branched coverings over closed three-braid and three-bridge knots

It is well known that every closed orientable three-manifold is given as a three-fold branched covering space branched over some knot. Then it is an interesting problem that for a given knot family what kind of manifold can be got as a three-fold irregular branched covering space. K. Murasugi showed that for a closed three-braid the manifold is a lens space of type (n,1). In this paper, we will give an another proof and an algorithm to determine n for a given knot. And for a three bridge knot, we will show that its covering space is a lens space of type (p,q), and give an algorithm to determine the pair of p, q.