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Non-left-orderable surgeries on twisted torus knots


Authors: Katherine Christianson, Justin Goluboff, Linus Hamann and Srikar Varadaraj
Journal: Proc. Amer. Math. Soc. 144 (2016), 2683-2696
MSC (2010): Primary 57M25; Secondary 20F60, 57M50
Published electronically: March 1, 2016
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Abstract: Boyer, Gordon, and Watson have conjectured that an irreducible rational homology 3-sphere is an L-space if and only if its fundamental group is not left-orderable. Since large classes of L-spaces can be produced from Dehn surgery on knots in $ S^3$, it is natural to ask what conditions on the knot group are sufficient to imply that the quotient associated to Dehn surgery is not left-orderable. Clay and Watson developed a criterion for determining the left-orderability of this quotient group and used it to verify the conjecture for surgeries on certain L-space twisted torus knots. We generalize a recent theorem of Ichihara and Temma to provide another such criterion. We then use this new criterion to generalize the results of Clay and Watson and to verify the conjecture for a much broader class of L-spaces obtained by surgery on twisted torus knots.


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Additional Information

Katherine Christianson
Affiliation: Department of Mathematics, Columbia University, New York, New York 10027
Email: mac2370@columbia.edu

Justin Goluboff
Affiliation: Department of Mathematics, Columbia University, New York, New York 10027
Email: goluboff@bc.edu

Linus Hamann
Affiliation: Department of Mathematics, Columbia University, New York, New York 10027
Email: dlh2145@columbia.edu

Srikar Varadaraj
Affiliation: Department of Mathematics, Columbia University, New York, New York 10027
Email: sv2423@columbia.edu

DOI: https://doi.org/10.1090/proc/12897
Keywords: Left-orderability, twisted torus knots, Dehn surgery
Received by editor(s): October 18, 2014
Received by editor(s) in revised form: May 15, 2015, and June 12, 2015
Published electronically: March 1, 2016
Additional Notes: The authors were partially funded by NSF grant DMS-0739392.
Communicated by: Martin Scharlemann
Article copyright: © Copyright 2016 American Mathematical Society