Non-left-orderable surgeries on twisted torus knots

Christianson, Katherine; Goluboff, Justin; Hamann, Linus; Varadaraj, Srikar

doi:10.1090/proc/12897

Non-left-orderable surgeries on twisted torus knots
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by Katherine Christianson, Justin Goluboff, Linus Hamann and Srikar Varadaraj

Proc. Amer. Math. Soc. 144 (2016), 2683-2696

DOI: https://doi.org/10.1090/proc/12897

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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