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Alternating links and left-orderability


Author: Joshua Evan Greene
Journal: Proc. Amer. Math. Soc. 146 (2018), 2707-2709
MSC (2010): Primary 57M05, 57M25
DOI: https://doi.org/10.1090/proc/13704
Published electronically: March 9, 2018
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Abstract: Let $ L \subset S^3$ denote an alternating link and $ \Sigma (L)$ its branched double-cover. We give a short proof of the fact that the fundamental group of $ \Sigma (L)$ admits a left-ordering iff $ L$ is an unlink. This result is originally due to Boyer-Gordon-Watson.


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Additional Information

Joshua Evan Greene
Affiliation: Department of Mathematics, Boston College, Chestnut Hill, Massachusetts 02467
Email: joshua.greene@bc.edu

DOI: https://doi.org/10.1090/proc/13704
Received by editor(s): February 13, 2017
Received by editor(s) in revised form: February 17, 2017
Published electronically: March 9, 2018
Additional Notes: This work was supported by NSF CAREER Award DMS-1455132 and an Alfred P. Sloan Research Fellowship.
Communicated by: David Futer
Article copyright: © Copyright 2018 American Mathematical Society

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