Virtual Legendrian isotopy

• Autorzy: Vladimir Chernov , Rustam Sadykov
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 57M27: Invariants of knots and 3-manifolds
• 57R17: Symplectic and contact topology
• 53D10: Contact manifolds, general

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2016
• Tom: 234
• Numer: 2
• Strony: 127-137

Daty

wydano

2016

Twórcy

autor

Vladimir Chernov

• Department of Mathematics, Dartmouth College, 6188 Kemeny Hall, Hanover, NH 03755, U.S.A.

autor

Rustam Sadykov

• Department of Mathematics, Kansas State University, 138 Cardwell Hall, Manhattan, KS 66506, U.S.A.

Identyfikatory

DOI

10.4064/fm969-10-2015