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What is a virtual link?

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

Keywords
virtual link, tetravalent graph, stable equivalence
Mathematical Subject Classification 2000
Primary: 57M25
Secondary: 57M27 57M15
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Publication
Received: 18 August 2002
Revised: 15 June 2003
Accepted: 23 October 2002
Published: 21 June 2003
Authors
Greg Kuperberg
Department of Mathematics
University of California
Davis, CA 95616
USA