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Virtual Biquandles

Authors
  • Kauffman, Louis
  • Manturov, Vassily Olegovich
Type
Preprint
Publication Date
Jun 21, 2005
Submission Date
Nov 10, 2004
Identifiers
arXiv ID: math/0411243
Source
arXiv
License
Unknown
External links

Abstract

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.

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