#### Volume 3, issue 1 (2003)

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### Greg Kuperberg

Algebraic & Geometric Topology 3 (2003) 587–591
 arXiv: math.GT/0208039
##### 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 $L\subset S×I$ in a thickened, compact, oriented surface $S$ such that the link complement $\left(S×I\right)\setminus L$ has no essential vertical cylinder.

##### Keywords
virtual link, tetravalent graph, stable equivalence
##### Mathematical Subject Classification 2000
Primary: 57M25
Secondary: 57M27 57M15