Non-left-orderable surgeries on 1-bridge braids

Abstract

Boyer, Gordon and Watson have conjectured that an irreducible rational homology [Formula: see text]-sphere is an L-space if and only if its fundamental group is not left-orderable. Since Dehn surgeries on knots in [Formula: see text] can produce large families of L-spaces, it is natural to examine the conjecture on these [Formula: see text]-manifolds. Greene, Lewallen and Vafaee have proved that all [Formula: see text]-bridge braids are L-space knots. In this paper, we consider three families of [Formula: see text]-bridge braids. First we calculate the knot groups and peripheral subgroups. We then verify the conjecture on the three cases by applying the criterion developed by Christianson, Goluboff, Hamann and Varadaraj, when they verified the same conjecture for certain twisted torus knots and generalized the criteria due to Clay and Watson and due to Ichihara and Temma.