What is a virtual link?

Greg Kuperberg

doi:10.2140/agt.2003.3.587

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Home > Journals > Algebr. Geom. Topol. > Volume 3 > Issue 1 > Article

2003 What is a virtual link?

Greg Kuperberg

Algebr. Geom. Topol. 3(1): 587-591 (2003). DOI: 10.2140/agt.2003.3.587

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