Algebraic & Geometric Topology

What is a virtual link?

Greg Kuperberg

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Several authors have recently studied virtual knots and links because they admit invariants arising from R–matrices. We prove that every virtual link is uniquely represented by a link LS×I in a thickened, compact, oriented surface S such that the link complement (S×I)L has no essential vertical cylinder.

Article information

Algebr. Geom. Topol., Volume 3, Number 1 (2003), 587-591.

Received: 18 August 2002
Revised: 15 June 2003
Accepted: 23 October 2002
First available in Project Euclid: 21 December 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 57M27 57M15

virtual link tetravalent graph stable equivalence


Kuperberg, Greg. What is a virtual link?. Algebr. Geom. Topol. 3 (2003), no. 1, 587--591. doi:10.2140/agt.2003.3.587.

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