Virtual biquandles

• Autorzy: Louis H. Kauffman , Vassily O. Manturov
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 57M25: Knots and links in S 3

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2005
• Tom: 188
• Numer: 1
• Strony: 103-146

Daty

wydano

2005

Twórcy

autor

Louis H. Kauffman

• Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 South Morgan St., Chicago, IL 60607-7045, U.S.A.

autor

Vassily O. Manturov

• Department of Mechanics and Mathematics, Moscow State University, 119992, GSP-2, Leninskie Gory, MSU, Moscow, Russia

Identyfikatory

DOI

10.4064/fm188-0-6