Virtual biquandles

Louis H. Kauffman; Vassily O. Manturov

Fundamenta Mathematicae (2005)

  • Volume: 188, Issue: 1, page 103-146
  • ISSN: 0016-2736

Abstract

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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 [Ma10], 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.

How to cite

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Louis H. Kauffman, and Vassily O. Manturov. "Virtual biquandles." Fundamenta Mathematicae 188.1 (2005): 103-146. <http://eudml.org/doc/282987>.

@article{LouisH2005,
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 [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 [Ma10], 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.},
author = {Louis H. Kauffman, Vassily O. Manturov},
journal = {Fundamenta Mathematicae},
keywords = {virtual knot; quandle; generalized Alexander polynomial},
language = {eng},
number = {1},
pages = {103-146},
title = {Virtual biquandles},
url = {http://eudml.org/doc/282987},
volume = {188},
year = {2005},
}

TY - JOUR
AU - Louis H. Kauffman
AU - Vassily O. Manturov
TI - Virtual biquandles
JO - Fundamenta Mathematicae
PY - 2005
VL - 188
IS - 1
SP - 103
EP - 146
AB - 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 [Ma10], 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.
LA - eng
KW - virtual knot; quandle; generalized Alexander polynomial
UR - http://eudml.org/doc/282987
ER -

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