Vol. 273, No. 1, 2015

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Vassiliev invariants of virtual Legendrian knots

Patricia Cahn and Asa Levi

Vol. 273 (2015), No. 1, 21–46

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.

Virtual knot, Legendrian knot, Vassiliev invariant
Mathematical Subject Classification 2010
Primary: 57M27
Received: 28 May 2013
Revised: 15 September 2013
Accepted: 23 September 2013
Published: 6 December 2014
Patricia Cahn
Department of Mathematics
University of Pennsylvania
David Rittenhouse Lab
209 South 33rd Street
Philadelphia, PA 19104-6395
United States
Asa Levi
Department of Mathematics
Dartmouth College
6188 Kemeny Hall
Hanover, PA 03755-3551
United States