Stable Equivalence of Knots on Surfaces and Virtual Knot Cobordisms

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dc.creatorCarter, J. Scott
dc.creatorKamada, Seiichi
dc.creatorSaito, Masahico
dc.date2000-08-16
dc.date.accessioned2026-07-07T04:36:49Z
dc.date.available2026-07-07T04:36:49Z
dc.descriptionWe introduce an equivalence relation, called stable equivalence, on knot diagrams and closed curves on surfaces. We give bijections between the set of abstract knots, the set of virtual knots, and the set of the stable equivalence classes of knot diagrams on surfaces. Using these bijections, we define concordance and link homology for virtual links. As an application, it is shown that Kauffman's example of a virtual knot diagram is not equivalent to a classical knot diagram.
dc.description12 pages, 9 figures
dc.identifierhttps://arxiv.org/abs/math/0008118
dc.identifierhttp://arxiv.org/abs/math/0008118
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59739
dc.subjectGeometric Topology
dc.subject57M25,57N70,57Q66
dc.titleStable Equivalence of Knots on Surfaces and Virtual Knot Cobordisms
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