Non-left-orderable surgeries on twisted torus knots (Q2796742)

The paper under review gives a new sufficient condition for the resulting manifold of Dehn surgery on a knot to have non-left-orderable fundamental group. It is an extension of a condition given by \textit{K. Ichihara} and \textit{Y. Temma} [J. Knot Theory Ramifications 24, No. 1, Article ID 1550003, 8 p. (2015; Zbl 1315.57022)]. The condition requires that the knot group is generated by two elements, and any homomorphism of the fundamental group of the surgered manifold into \(\text{Homeo}^+(\mathbb{R})\), the group of order-preserving homeomorphisms of the real line, satisfies a certain extra condition. However, the authors can show that for two new classes of twisted torus knots which admit \(L\)-space surgeries, any Dehn surgery whose slope is bigger than a certain number depending on the parameters of the twisted torus knot, yields a \(3\)-manifold whose fundamental group is not left-orderable.