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.

中文翻译：

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1-bridge 辫子上的非左侧可订购手术

Boyer、Gordon 和 Watson 推测，一个不可约的有理同调 [公式：见正文]-球体是 L-空间当且仅当其基本群不是左可排序的。由于对 [公式：见文本] 中的结进行 Dehn 手术可以产生大量的 L 空间族，因此很自然地检查对这些 [公式：见文本] 流形的猜想。Greene、Lewallen 和 Vafaee 已经证明所有 [公式：见正文]-桥辫都是 L 空间结。在本文中，我们考虑了三个族[公式：见正文]-桥辫。首先我们计算节点组和外围子组。然后，我们通过应用 Christianson、Goluboff、Hamann 和 Varadaraj 开发的标准来验证这三种情况的猜想，