A+ CATEGORY SCIENTIFIC UNIT

Virtual biquandles

Volume 188 / 2005

Louis H. Kauffman, Vassily O. Manturov 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.

Authors

  • Louis H. KauffmanDepartment of Mathematics
    Statistics and Computer Science
    University of Illinois at Chicago
    851 South Morgan St.
    Chicago, IL 60607-7045, U.S.A.
    e-mail
  • Vassily O. ManturovDepartment of Mechanics and Mathematics
    Moscow State University
    119992, GSP-2, Leninskie Gory
    MSU, Moscow, Russia
    e-mail

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