Virtual knot cobordism and the affine index polynomial

Louis H. Kauffman

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

This paper studies cobordism and concordance for virtual knots. We define the affine index polynomial, prove that it is a concordance invariant for knots and links (explaining when it is defined for links), show that it is also invariant under certain forms of labeled cobordism and study a number of examples in relation to these phenomena. Information on determinations of the four-ball genus of some virtual knots is obtained by via the affine index polynomial in conjunction with results on the genus of positive virtual knots using joint work with Dye and Kaestner.

Original languageEnglish
Article number1843017
Number of pages29
JournalJournal of Knot Theory and its Ramifications
Volume27
Issue number11
DOIs
Publication statusPublished - 1 Oct 2018

Keywords

  • affine index polynomial
  • cobordism
  • concordance
  • invariant
  • Khovanov homology
  • Knot
  • knotoid
  • labeled cobordism
  • link
  • Rasmussen invariant
  • virtual knot
  • INVARIANT

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