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Vassiliev invariants
of virtual Legendrian knots
Patricia Cahn and Asa Levi |
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Vol. 273 (2015), No. 1, 21–46
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Abstract |
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We introduce a theory of virtual Legendrian knots. A virtual Legendrian knot is a cooriented wavefront on an oriented surface up to Legendrian isotopy of its lift to the unit cotangent bundle and stabilization and destabilization of the surface away from the wavefront. We show that the groups of Vassiliev invariants of virtual Legendrian knots and of virtual framed knots are isomorphic. In particular, Vassiliev invariants cannot be used to distinguish virtual Legendrian knots that are isotopic as virtual framed knots and have equal virtual Maslov numbers. |
Keywords
Virtual knot, Legendrian knot, Vassiliev invariant
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Mathematical Subject Classification 2010
Primary: 57M27
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Milestones
Received: 28 May 2013
Revised: 15 September 2013
Accepted: 23 September 2013
Published: 6 December 2014
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Authors |
| Patricia Cahn | |
| Department of Mathematics University of Pennsylvania David Rittenhouse Lab 209 South 33rd Street Philadelphia, PA 19104-6395 United States |
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| Asa Levi | |
| Department of Mathematics Dartmouth College 6188 Kemeny Hall Hanover, PA 03755-3551 United States |
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