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Virtual Legendrian Isotopy
An elementary stabilization of a Legendrian link in the spherical
cotangent bundle of a surface is a surgery that results in
attaching a handle to along two discs away from the image in of the
projection of the link . A virtual Legendrian isotopy is a composition of
stabilizations, destabilizations and Legendrian isotopies.
In contrast to Legendrian knots, virtual Legendrian knots enjoy the property
that there is a bijective correspondence between the virtual Legendrian knots
and the equivalence classes of Gauss diagrams.
We study virtual Legendrian isotopy classes of Legendrian links and show that
every such class contains a unique irreducible representative. In particular we
get a solution to the following conjecture of Cahn, Levi and the first author:
two Legendrian knots in that are isotopic as virtual Legendrian knots
must be Legendrian isotopic in Comment: 10 pages, 4 figur
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