Virtual Knot Theory and Virtual Knot Cobordism

Louis H. Kauffman

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review


This paper is an introduction to virtual knot theory and virtual knot cobordism [37, 39]. Non-trivial examples of virtual slice knots are given and determinations of the four-ball genus of positive virtual knots are explained in relation to joint work with Dye and Kaestner [12]. We study the affine index polynomial [38], prove that it is a concordance invariant, show that it is invariant also under certain forms of labeled cobordism and study a number of examples in relation to these phenomena. In particular we show how a mod-2 version of the affine index polynomial is a concordance invariant of flat virtual knots and links, and explore a number of examples in this domain.

Original languageEnglish
Title of host publicationKnots, Low-Dimensional Topology and Applications - Knots in Hellas, International Olympic Academy, 2016
EditorsColin C. Adams, Cameron McA. Gordon, Vaughan F.R. Jones, Louis H. Kauffman, Sofia Lambropoulou, Kenneth C. Millett, Jozef H. Przytycki, Jozef H. Przytycki, Renzo Ricca, Radmila Sazdanovic
PublisherSpringer New York LLC
Number of pages48
ISBN (Print)9783030160302
Publication statusPublished - 1 Jan 2019
EventInternational Olympic Academy, 2016 - Ancient Olympia, Greece
Duration: 17 Jul 201623 Jul 2016

Publication series

NameSpringer Proceedings in Mathematics and Statistics
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017


ConferenceInternational Olympic Academy, 2016
CityAncient Olympia


  • Affine index polynomial
  • Arrow polynomial
  • Bracket polynomial
  • Cobordism
  • Concordance
  • Graph
  • Invariant
  • Knot
  • Link
  • Parity bracket polynomial
  • Virtual knot

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