Table of Contents
Geometry
Volume 2013 (2013), Article ID 549198, 9 pages
http://dx.doi.org/10.1155/2013/549198
Research Article

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

Dipartimento di Matematica, Università di Modena e Reggio E., Via Campi 213/B, 41100 Modena, Italy

Received 19 October 2012; Revised 12 March 2013; Accepted 18 March 2013

Academic Editor: Michel Planat

Copyright © 2013 Agnese Ilaria Telloni. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.