Left orderability for surgeries on the [1,1,2,2,2j] two-bridge knots

Abstract

Let [Formula: see text] be a [Formula: see text]-homology solid torus. In this paper, we give a cohomological criterion for the existence of an interval of left orderable Dehn surgeries on [Formula: see text]. We apply this criterion to prove that the two-bridge knot that corresponds to the continued fraction [Formula: see text] for [Formula: see text] admits an interval of left orderable Dehn surgeries. This family of two-bridge knots gives some positive evidence for a question of Xinghua Gao.