Virtual Biquandles

By Louis H. Kauffman, V. Manturov. 2004

60 citations recorded by the source corpus.

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 [KR], [FJK], the virtual quandle [Ma2], the ideas of quaternion biquandles by Roger Fenn and Andrew Bartholomew [BF], the concepts and properties of long virtual knots [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.

Subfields: Computational Mechanics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/d9fc02f0eabb7eac30702b23bd6c5c4b9510ca58

How researchers see this paper

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1. J. Vo
2. Sam Nelson
3. Louis H. Kauffman
4. Pvremysl Jedlivcka

Citations in the corpus

• Matrices and finite biquandles (2006, background): “See [13] for more on the universal algebra of biquandles.”