Algebraic and Geometric Topology 3 (2003), paper no. 20, pages 587-591.

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 in S X I, a thickened, compact, oriented surface S, such that the link complement (S X I) - L has no essential vertical cylinder.

Keywords. Virtual link, tetravalent graph, stable equivalence

AMS subject classification. Primary: 57M25. Secondary: 57M27 57M15.

DOI: 10.2140/agt.2003.3.587

E-print: arXiv:math.GT/0208039

Submitted: 18 August 2002. (Revised: 15 June 2003.) Accepted: 23 October 2002. Published: 21 June 2003.

Notes on file formats

Greg Kuperberg
Department of Mathematics, University of California
Davis, CA 95616, USA

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