Virtual Knot Theory

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dc.creatorKauffman, Louis H.
dc.date1998-11-05
dc.date2006-05-22
dc.date.accessioned2026-07-07T06:34:30Z
dc.date.available2026-07-07T06:34:30Z
dc.descriptionVirtual knot theory is a generalization (discovered by the author in 1996) of knot theory to the study of all oriented Gauss codes. (Classical knot theory is a study of planar Gauss codes.) Graph theory studies non-planar graphs via graphical diagrams with virtual crossings. Virtual knot theory studies non-planar Gauss codes via knot diagrams with virtual crossings. This paper gives basic results and examples (such as non-trivial virtual knots with trivial Jones polynomial), studies fundamental group and quandles of virtual knots, extensions of the bracket and Jones polynomials, quantum link invariants with virtual framings, Vassiliev invariants and applications to knots in thickened surfaces.
dc.descriptionLaTeX, 53 pages, 25 figures
dc.identifierhttps://arxiv.org/abs/math/9811028
dc.identifierhttp://arxiv.org/abs/math/9811028
dc.identifierEuropean J. Comb. (1999) Vol. 20, 663-690
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/99546
dc.subjectGeometric Topology
dc.subjectQuantum Algebra
dc.titleVirtual Knot Theory
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