JOURNAL ARTICLE

Multi-virtual knot theory.

  • Published In: Journal of Knot Theory & Its Ramifications, 2025, v. 34, n. 14. P. 1 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: Kauffman, Louis H. 3 of 3

Abstract

In this paper, we generalize virtual knot theory to multi-virtual knot theory where there are a multiplicity of virtual crossings. Each virtual crossing type can detour over the other virtual crossing types, and over classical or immersed crossings. New invariants of multi-virtual knots and links are introduced and new problems that arise are described. We show how the extensions of the Penrose coloring evaluation for trivalent plane graphs and our generalizations of this to non-planar graphs and arbitrary numbers of colors acts as a motivation for the construction of the multi-virtual theory. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:Journal of Knot Theory & Its Ramifications. 2025/12, Vol. 34, Issue 14, p1
  • Document Type:Article
  • Subject Area:Mathematics
  • Publication Date:2025
  • ISSN:0218-2165
  • DOI:10.1142/S0218216525400024
  • Accession Number:189942379
  • Copyright Statement:Copyright of Journal of Knot Theory & Its Ramifications is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Looking to go deeper into this topic? Look for more articles on EBSCOhost.