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

We consider cyclic branched coverings of a 3-parameter family of rational knots in S 3 and study the left orderability of their fundamental groups. We first compute the nonabelian SL 2 (ℂ) -character varieties of the rational knots C (2 p , 2 m , 2 n + 1) in the Conway notation, where p , m , n 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 C (2 p , 2 m , 2 n + 1). [ABSTRACT FROM AUTHOR]