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.
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