Non-left-orderable surgeries on L-space twisted torus knots
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Abstract:
We show that if $K$ is an L-space twisted torus knot $T^{l,m}_{p,pk \pm 1}$ with $p \ge 2$, $k \ge 1$, $m \ge 1$, and $1 \le l \le p-1$, then the fundamental group of the $3$-manifold obtained by $\frac {r}{s}$-surgery along $K$ is not left-orderable whenever $\frac {r}{s} \ge 2 g(K) -1$, where $g(K)$ is the genus of $K$.References
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Additional Information
- Anh T. Tran
- Affiliation: Department of Mathematical Sciences, The University of Texas at Dallas, Richardson, Texas 75080
- MR Author ID: 922985
- Email: att140830@utdallas.edu
- Received by editor(s): March 16, 2019
- Received by editor(s) in revised form: April 27, 2019, and April 30, 2019
- Published electronically: July 30, 2019
- Additional Notes: The author was partially supported by a grant from the Simons Foundation (#354595).
- Communicated by: David Futer
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 447-456
- MSC (2010): Primary 57M27; Secondary 57M25
- DOI: https://doi.org/10.1090/proc/14701
- MathSciNet review: 4042866