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VIRTUAL BRAIDS AND THE L-MOVE

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

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SOFIA LAMBROPOULOU

Department of Mathematics, National Technical University of Athens, Zografou campus, GR-157 80 Athens, Greece

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https://doi.org/10.1142/S0218216506004750Cited by:42 (Source: Crossref)

Abstract

In this paper we prove a Markov theorem for virtual braids and for analogs of this structure including flat virtual braids and welded braids. The virtual braid group is the natural companion to the category of virtual knots, just as the Artin braid group is the natural companion to classical knots and links. In this paper we follow L-move methods to prove the Virtual Markov theorems. One benefit of this approach is a fully local algebraic formulation of the theorems in each category.

Keywords:

AMSC: 57M25

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