About some infinite family of 2-bridge knots and 3-manifolds
The author studies the topological and algebraic properties of some series of cyclically presented groups which arise as fundamental groups of closed connected orientable 3-manifolds. These manifolds are presented by polyhedron schemata, that is, they are obtained by pairwise identifications of polygons in special tessellations of the boundary of a 3-ball. Then the author proves that the considered manifolds are cyclic coverings of the 3-sphere branched along the 2-bridge knots \((k+1)_2\) or \((k+1)_1\), according as \(k\) is even or odd, respectively. Finally, it is also shown that these manifolds are 2-fold branched coverings of the 3-sphere branched over special \(n\)-periodic knots.
scientific article; zbMATH DE number 1529553