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July, 2021 Left orderable surgeries of double twist knots
Anh T. TRAN
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J. Math. Soc. Japan 73(3): 753-765 (July, 2021). DOI: 10.2969/jmsj/84058405

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 $K$.

Funding Statement

The author has been partially supported by a grant from the Simons Foundation (#354595).

Citation

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Anh T. TRAN. "Left orderable surgeries of double twist knots." J. Math. Soc. Japan 73 (3) 753 - 765, July, 2021. https://doi.org/10.2969/jmsj/84058405

Information

Received: 21 January 2020; Published: July, 2021
First available in Project Euclid: 15 October 2020

Digital Object Identifier: 10.2969/jmsj/84058405

Subjects:
Primary: 57M27
Secondary: 57M25

Rights: Copyright ©2021 Mathematical Society of Japan

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Vol.73 • No. 3 • July, 2021
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