Left orderable surgeries of double twist knots

Anh T. Tran

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arXiv · 1911.03798

Left orderable surgeries of double twist knots

Anh T. Tran

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Abstract

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 $K$.

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BibTeX RIS

Anh T. Tran. 2019-11-09. Left orderable surgeries of double twist knots. https://arxiv.org/abs/1911.03798

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