|
Organizers |
Virtual Legenedrian Isotopy
by
R. Sadykov
Dartmouth College
Coauthors: V. Chernov
An elementary stabilization of a Legendrian knot L in the spherical cotangent bundle 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.
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 Chernov: two Legendrian knots in the spherical cotangent bundle of the 2-sphere that are isotopic as virtual Legendrian knots must be Legendrian isotopic.
Date received: March 6, 2015
Copyright © 2015 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbkp-22.