Virtual Legendrian isotopy

@article{VladimirChernov2016,
abstract = { An elementary stabilization of a Legendrian knot L in the spherical cotangent bundle ST*M of a surface M is a surgery that results in attaching a handle to M along two discs away from the image in M of the projection of the knot L. A virtual Legendrian isotopy is a composition of stabilizations, destabilizations and Legendrian isotopies. A class of virtual Legendrian isotopy is called a virtual Legendrian knot. 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 knots 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 ST*S² that are isotopic as virtual Legendrian knots must be Legendrian isotopic in ST*S². },
author = {Vladimir Chernov, Rustam Sadykov},
journal = {Fundamenta Mathematicae},
keywords = {Legendrian links; stable isotopy; virtual Legendrian links},
language = {eng},
number = {2},
pages = {127-137},
title = {Virtual Legendrian isotopy},
url = {http://eudml.org/doc/286296},
volume = {234},
year = {2016},
}

TY - JOUR
AU - Vladimir Chernov
AU - Rustam Sadykov
TI - Virtual Legendrian isotopy
JO - Fundamenta Mathematicae
PY - 2016
VL - 234
IS - 2
SP - 127
EP - 137
AB - An elementary stabilization of a Legendrian knot L in the spherical cotangent bundle ST*M of a surface M is a surgery that results in attaching a handle to M along two discs away from the image in M of the projection of the knot L. A virtual Legendrian isotopy is a composition of stabilizations, destabilizations and Legendrian isotopies. A class of virtual Legendrian isotopy is called a virtual Legendrian knot. 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 knots 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 ST*S² that are isotopic as virtual Legendrian knots must be Legendrian isotopic in ST*S².
LA - eng
KW - Legendrian links; stable isotopy; virtual Legendrian links
UR - http://eudml.org/doc/286296
ER -