On 3-fold irregular branched covering spaces of pretzel knots (Q1079234)

It is well known that any orientable closed 3-manifold is a 3-fold irregular branched covering space of a 3-sphere branched along a knot. It is an interesting problem to know which 3-manifold can be a 3-fold irregular branched covering space of a given knot. In this paper, the authors show the following theorem using the result by \textit{J. M. Montesinos Amilibia} [Rev. Mat. Hisp.-Am., IV. Ser. 32, 33-51 (1972; Zbl 0235.55003)]. Theorem. Each 3-fold irregular branched covering space of a 3-sphere branched along a pretzel knot, if it exists, is isomorphic to a 3-sphere, a lens space of type (p,1) for some nonnegative integer p, or a connected sum of those spaces.