Cyclic Branched Coverings Over Some Classes of (1,1)-Knots

Abstract

We construct a 4-parametric family of combinatorial closed 3-manifolds, obtained by glueing together in pairs the boundary faces of polyhedral 3-balls. Then, we obtain geometric presentations of the fundamental groups of these manifolds and determine the corresponding split extension groups. Finally, we prove that the considered manifolds are cyclic coverings of the 3-sphere branched over well-specified -knots, including torus knots and Montesinos knots.