Virtual biquandles
Volume 188 / 2005
Fundamenta Mathematicae 188 (2005), 103-146
MSC: Primary 57M25.
DOI: 10.4064/fm188-0-6
Abstract
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 \cite{KR}, \cite{FJK}, the virtual quandle \cite{Ma2}, the ideas of quaternion biquandles by Roger Fenn and Andrew Bartholomew \cite{BF}, the concepts and properties of long virtual knots \cite{Ma11}, 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.
