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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Non-left-orderable surgeries on twisted torus knots
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by Katherine Christianson, Justin Goluboff, Linus Hamann and Srikar Varadaraj PDF
Proc. Amer. Math. Soc. 144 (2016), 2683-2696 Request permission

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.
References
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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
  • 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
  • © Copyright 2016 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 2683-2696
  • MSC (2010): Primary 57M25; Secondary 20F60, 57M50
  • DOI: https://doi.org/10.1090/proc/12897
  • MathSciNet review: 3477086