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

Abstract EN

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 (1,1)-knots, including torus knots and Montesinos knots.