Knot contact homology detects cabled, composite, and torus knots
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- by Cameron Gordon and Tye Lidman PDF
- Proc. Amer. Math. Soc. 145 (2017), 5405-5412 Request permission
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).References
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Additional Information
- Cameron Gordon
- Affiliation: Department of Mathematics, The University of Texas at Austin, Austin, TX, 78712, USA
- MR Author ID: 75435
- Email: gordon@math.utexas.edu
- Tye Lidman
- Affiliation: Department of Mathematics, North Caroline State University, Raleigh, NC, 27603, USA
- MR Author ID: 808881
- Email: tlild@math.ncsu.edu
- 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
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 5405-5412
- MSC (2010): Primary 57M25, 57M27, 57R17
- DOI: https://doi.org/10.1090/proc/13643
- MathSciNet review: 3717966