On invariants of virtual links
type: Item
instance of: scholarly article
title: On invariants of virtual links
zbMATH Open document ID: 1003.57005
DOI: 10.1023/A:1016258728022
published in: Acta Applicandae Mathematicae
publication date: 2002-08-19T00:00:00Z
review text: Virtual knot theory is a generalization of classical knot theory. Virtual links have diagrams which contain in addition to the classical crossings (where one arc passes over another) virtual crossings, that is points of self-intersections of the arcs in the diagram. The equivalence of virtual knots and links is defined combinatorically by generalized Reidemeister moves involving also the virtual crossings. In this paper the author generalizes classical link invariants (such as the knot quandle, the knot fundamental group, the Alexander module and coloring invariants) to virtual link invariants. His work generalizes a construction of a knot quandle for virtual knots by \textit{L. H. Kauffman} [Eur. J. Comb. 20, No. 7, 663-690 (1999; Zbl 0938.57006)] to a virtual quandle \(Q\). From \(Q\) a virtual Alexander module can be computed. That in turn leads to a definition of a virtual Alexander polynomial that has no analogue in the classical case (i.e. it vanishes on classical links).
reviewed by: Claus Ernst
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 1783465
zbMATH Keywords: virtual knot
zbMATH Keywords: virtual link
zbMATH Keywords: quandle
zbMATH Keywords: fundamental group
zbMATH Keywords: polynomial invariant
author: V. O. Manturov
MaRDI profile type: Publication
full work available at URL: a:1016258728022
OpenAlex ID: W2472181540
description: scientific article; zbMATH DE number 1783465