Left orderability and cyclic branched coverings of rational knots C(2p,2m,2n + 1)

Abstract

We consider cyclic branched coverings of a 3-parameter family of rational knots in [Formula: see text] and study the left orderability of their fundamental groups. We first compute the nonabelian [Formula: see text]-character varieties of the rational knots [Formula: see text] in the Conway notation, where [Formula: see text] are integers. We then study real points on these varieties and finally use them to determine the left orderability of the fundamental groups of cyclic branched coverings of [Formula: see text].