English

Bi-oriented Quantum Algebras, and a Generalized Alexander Polynomial for Virtual Links

Geometric Topology 2007-05-23 v2 Rings and Algebras

Abstract

This paper discusses the construction of a generalized Alexander polynomial for virtual knots and links, and the reformulation of this invariant as a quantum link invariant. The algebraic background for the generalized Alexander module is formulated in terms of the biquandle, a generalization of the quandle of David Joyce (which, in turn, is a generalization of the fundamental group of the knot or link). We then introduce the concept of a bi-oriented quantum algebra which provides an algebraic context for the associated quantum invariant.

Keywords

Cite

@article{arxiv.math/0112280,
  title  = {Bi-oriented Quantum Algebras, and a Generalized Alexander Polynomial for Virtual Links},
  author = {Louis H. Kauffman and David E. Radford},
  journal= {arXiv preprint arXiv:math/0112280},
  year   = {2007}
}

Comments

LaTeX document, 34 pages, 13 figures, in text LaTeX graphics

R2 v1 2026-07-22T16:42:23.889Z