Virtual Biquandles
几何拓扑
2007-05-23 v5 量子代数
摘要
In the present paper, we describe new approaches for constructing virtual knot invariants. The main background of this paper comes from formulating and bringing together the ideas of biquandle (Kauffman and Radford) the virtual quandle (Manturov), the ideas of quaternion biquandles by Roger Fenn and Andrew Bartholomew, the concepts and properties of long virtual knots (Manturov), and other ideas in the interface between classical and virtual knot theory. In the present paper we present a new algebraic construction of virtual knot invariants, give various presentations of it, and study several examples. Several conjectures and unsolved problems are presented throughout the paper.
关键词
引用
@article{arxiv.math/0411243,
title = {Virtual Biquandles},
author = {Louis Kauffman and Vassily Olegovich Manturov},
journal= {arXiv preprint arXiv:math/0411243},
year = {2007}
}