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Knot contact homology detects cabled, composite, and torus knots


Authors: Cameron Gordon and Tye Lidman
Journal: Proc. Amer. Math. Soc.
MSC (2010): Primary 57M25, 57M27, 57R17
DOI: https://doi.org/10.1090/proc/13643
Published electronically: June 16, 2017
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Abstract: Knot contact homology is an invariant of knots derived from Legendrian contact homology which has numerous connections to the knot group. We use basic properties of knot groups to prove that knot contact homology detects every torus knot. Further, if the knot contact homology of a knot is isomorphic to that of a cable (respectively composite) knot, then the knot is a cable (respectively composite).


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Additional Information

Cameron Gordon
Affiliation: Department of Mathematics, The University of Texas at Austin, Austin, TX, 78701, USA
Email: gordon@math.utexas.edu

Tye Lidman
Affiliation: Department of Mathematics, North Caroline State University, Raleigh, NC, 27603, USA
Email: tlild@math.ncsu.edu

DOI: https://doi.org/10.1090/proc/13643
Received by editor(s): November 3, 2015
Received by editor(s) in revised form: December 28, 2016
Published electronically: June 16, 2017
Additional Notes: The first author was partially supported by NSF Grant DMS-1309021. The second author was partially supported by NSF Grant DMS-1148490.
Communicated by: Kevin Whyte
Article copyright: © Copyright 2017 American Mathematical Society