Boyer, Gordon, and Watson have conjectured that an irreducible rationalhomology 3-sphere is an L-space if and only if its fundamental group is notleft-orderable. Since Dehn surgeries on knots in $S^3$ can produce largefamilies of L-spaces, it is natural to examine the conjecture on these3-manifolds. Greene, Lewallen, and Vafaee have proved that all 1-bridge braidsare L-space knots. In this paper, we consider three families of 1-bridgebraids. First we calculate the knot groups and peripheral subgroups. We thenverify the conjecture on the three cases by applying the criterion developed byChristianson, Goluboff, Hamann, and Varadaraj, when they verified the sameconjecture for certain twisted torus knots and generalized the criteria of Clayand Watson and of Ichihara and Temma.
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机译：Boyer，Gordon和Watson猜测，如果它的基本组是未订购的，那么如果才有一个不可挽回的理性主题3-Speol是L-Space。由于在$ S ^ 3 $上的德文手术，因此可以产生L-Spaces的大洁草，因此在这3歧管上检查猜想是自然的。 Greene，Lewallen和Vafaee证明了所有1桥辫子L空间结。在本文中，我们考虑了三个桥梁的三个家庭。首先，我们计算结组和外围子组。然后，我们通过应用Bychristianson，Goluboff，Hamann和Varadaraj的标准，在三种情况下，当他们验证某些扭曲的圆环结的SameConjecture并推广克莱和沃森和Ichihara和Temma的标准时，我们验证了这三种情况。
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