A rational number $r$ is called a left orderable slope of a knot $K \subset S^3$ if the 3-manifold obtained from $S^3$ by $r$-surgery along $K$ has left orderable fundamental group. In this paper we consider the double twist knots $C(k, l)$ in the Conway notation. For any positive integers $m$ and $n$, we show that if $K$ is a double twist knot of the form $C(2m, -2n)$, $C(2m+1, 2n)$ or $C(2m+1, -2n)$ then there is an explicit unbounded interval $I$ such that any rational number $r \in I$ is a left orderable slope of $K$.
The author has been partially supported by a grant from the Simons Foundation (#354595).
"Left orderable surgeries of double twist knots." J. Math. Soc. Japan 73 (3) 753 - 765, July, 2021. https://doi.org/10.2969/jmsj/84058405