Left-orderability and exceptional Dehn surgery on two-bridge knots (Q2867793)

The authors study the left-orderability of the fundamental group of graph manifolds that come from exceptional surgeries of hyperbolic 2-bridge knots. It turns out that one of the Seifert fibered pieces of such a manifold is the exterior of the \((2,p)\)-torus knot. By using an isolated ordering of the \((2,p)\)-torus knot group [\textit{A. Navas}, J. Algebra 328, No. 1, 31--42 (2011; Zbl 1215.06010); \textit{T. Ito}, ibid. 374, 42--58 (2013; Zbl 1319.06012)] and Bludov-Glass' theorem on orderability of amalgamated products [\textit{V. Bludov} and \textit{A. Glass}, Proc. Lond. Math. Soc. (3) 99, No. 3, 585--608 (2009; Zbl 1185.06016)], the authors prove that the fundamental group of such a graph manifold is left-orderable. As a consequence, they show that the fundamental group of a 3-manifold obtained by exceptional surgery on a hyperbolic 2-bridge knot is always left-orderable.NEWLINENEWLINEFor the entire collection see [Zbl 1272.57002].