Left-orderability, branched covers and double twist knots

Abstract

For some families of two-bridge knots, including double twist knots with genus at least four, we determine precisely the set of integers n > 1 n>1 such that the fundamental group of the n n -fold cyclic branched cover of the 3-sphere along these knots is left-orderable. There are knots, including the figure-eight knot, for which this set is empty. We give the first class of hyperbolic knots, not of this type, for which these integers can be completely determined.