Virtual braids

Tom 184 / 2004

Louis H. Kauffman, Sofia Lambropoulou Fundamenta Mathematicae 184 (2004), 159-186 MSC: Primary 57M25. DOI: 10.4064/fm184-0-11


This paper gives a new method for converting virtual knots and links to virtual braids. Indeed, the braiding method given here is quite general and applies to all the categories in which braiding can be accomplished. This includes the braiding of classical, virtual, flat, welded, unrestricted, and singular knots and links. We also give reduced presentations for the virtual braid group and for the flat virtual braid group (as well as for other categories). These reduced presentations are based on the fact that these virtual braid groups for $n$ strands are generated by a single braiding element plus the generators of the symmetric group on $n$ letters.


  • 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.
  • Sofia LambropoulouDepartment of Mathematics
    National Technical University of Athens
    Zografou Campus, GR-157 80 Athens, Greece
    Laboratoire de Mathématiques Nicolas Oresme
    Université de Caen
    F-14032 Caen Cedex, France

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