Virtual Knot Theory --Unsolved Problems

This paper is an introduction to the theory of virtual knots and links and it gives a list of unsolved problems in this subject.Comment: 33 pages, 7 figures, LaTeX documen

Unsolved Problems in Virtual Knot Theory and Combinatorial Knot Theory

This paper is a concise introduction to virtual knot theory, coupled with a list of research problems in this field.Comment: 65 pages, 24 figures. arXiv admin note: text overlap with arXiv:math/040542

Virtual Biquandles

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