What is a virtual link?

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

Keywords

virtual link, tetravalent graph, stable equivalence

Mathematical Subject Classification 2000

Primary: 57M25

Secondary: 57M27 57M15

References

Forward citations

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

Volume 3, issue 1 (2003)

Greg Kuperberg