Topology Atlas | Conferences

Knots in Washington XL in memory of Sergei Duzhin (1956-2015)
March 9-11, 2015
George Washington University and Georgetown University
Washington, DC, USA

Organizers
Valentina Harizanov (GWU), Paul Kainen (Georgetown U.), Jozef H. Przytycki (GWU), Yongwu Rong (GWU), Radmila Sazdanovic (NCSU), Alexander Shumakovitch (GWU), Hao Wu (GWU)

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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.