## Algebraic & Geometric Topology

### What is a virtual link?

Greg Kuperberg

#### Abstract

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 $L⊂S×I$ in a thickened, compact, oriented surface $S$ such that the link complement $(S×I)∖L$ has no essential vertical cylinder.

#### Article information

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

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

https://projecteuclid.org/euclid.agt/1513882385

Digital Object Identifier
doi:10.2140/agt.2003.3.587

Mathematical Reviews number (MathSciNet)
MR1997331

Zentralblatt MATH identifier
1031.57010

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

#### Citation

Kuperberg, Greg. What is a virtual link?. Algebr. Geom. Topol. 3 (2003), no. 1, 587--591. doi:10.2140/agt.2003.3.587. https://projecteuclid.org/euclid.agt/1513882385

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