Vassiliev Invariants of Virtual Legendrian Knots

Authors

Patricia Cahn, University of PennsylvaniaFollow
Asa Levi, Dartmouth College

Document Type

Article

Publication Date

2015

Publication Title

Pacific Journal of Mathematics

Abstract

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

Volume

273

Issue

1

First Page

21

Last Page

46

DOI

10.2140/pjm.2015.273.21

Rights

© the authors

Comments

Archived as published.

Recommended Citation

Cahn, Patricia and Levi, Asa, "Vassiliev Invariants of Virtual Legendrian Knots" (2015). Mathematics Sciences: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/55