\begin{thebibliography}{BN2}
\backrefparscanfalse\renewcommand*\backref[1]{See pp.~#1.}%
\renewcommand*\backrefalt[4]{\ifcase #1\or In page #2.\else In pages #2.\fi}

\bibitem[Ar]{Artin:TheoryOfBraids} E.~Artin,
  {\em Theory of Braids,}
  Ann.\ of Math.\ {\bf 48-1} (1947) 101--126. \backrefprint

\bibitem[ABMW1]{AudoxBellingeriMeilhanWagner:WeldedStringLinks}
  B.~Audoux, P.~Bellingeri, J-B.~Meilhan, and E.~Wagner,
  {\em Homotopy Classification of Ribbon Tubes and Welded String Links,}
  Ann.\ Sc.\ Norm.\ Super.\ Pisa Cl.\ Sci.\ {\bf 17-1} (2017) 713--761, \arXiv{1407.0184}.
  \backrefprint

\bibitem[ABMW2]{AudoxBellingeriMeilhanWagner:UVWHomotopy}
  B.~Audoux, P.~Bellingeri, J-B.~Meilhan, and E.~Wagner,
  {\em On Usual, Virtual, and Welded Knotted Objects up to Homotopy,}
  J.\ Math.\ Soc.\ Japan {\bf 69-3} (2017) 1079--1097, \arXiv{1507.00202}. \backrefprint

\bibitem[AM]{AudouxMeilhan:PeripheralSystems} B.~Audoux and J-B.~Meilhan,
  {\em Characterization of the Reduced Peripheral System of Links,}
  \arXiv{1904.04763}. \backrefprint

\bibitem[BN1]{Bar-Natan:glN} D.~Bar-Natan,
  \href{http://www.math.toronto.edu/~drorbn/papers/glN/glN.pdf}{
    {\em Vassiliev and Quantum Invariants of Braids,}
  }
  in Proc.\ of Symp.\ in Appl.\ Math.\ {\bf 51} (1995) {\em The Interface
  of Knots and Physics}, (L.~H.~Kauffman, ed.), Amer.\ Math.\ Soc.,
  Providence, \arXiv{q-alg/9607001}. \backrefprint

\bibitem[BN2]{Caen} D.~Bar-Natan and others,
  {\em Caen Workshop on v- and w-Knotted Objects,}
  2012 workshop in Caen. Videotaped lectures at
  \url{http://www.math.toronto.edu/~drorbn/Talks/Caen-1206/}.
  \backrefprint

\bibitem[BN3]{MasterClass} D.~Bar-Natan,
  {\em (u, v, and w knots)$\times$(topology, combinatorics, low algebra,
  and high algebra),} 2013 master class in Aarhus. Videotaped lectures
  at \url{http://www.math.toronto.edu/~drorbn/Talks/Aarhus-1305/}.
  \backrefprint

\bibitem[BN4]{KBH} D.~Bar-Natan,
  {\em
    \href{http://www.math.toronto.edu/~drorbn/papers/KBH/}{Balloons and
      Hoops and their Universal Finite Type Invariant, BF
      Theory, and an Ultimate Alexander Invariant,}
  }
  Acta Mathematica Vietnamica {\bf 40-2} (2015) 271--329, \arXiv{1308.1721}.
  \backrefprint

\bibitem[BN5]{Talk:OU} D.~Bar-Natan,
  {\em Over-then-Under-tangles and the Drinfel'd Double,} talk
  at \href{http://drorbn.net/m19}{\em Expansions, Lie Algebras,
  and Invariants,} Workshop at CRM, Montreal, July 2019. Video at
  \url{http://drorbn.net/m19/#Bar-Natan-4}. \backrefprint

\bibitem[BN6]{Talk:GvI} D.~Bar-Natan,
  {\em Geography vs.\ Identity,} talk
  at the \href{https://winter19.cms.math.ca/}{\em CMS Winter 2019 Meeting,}
  in Toronto, December 2019. Handout and video at
  \url{http://drorbn.net/to19/#1}. \backrefprint

\bibitem[BN7]{WKO4} D.~Bar-Natan,
  {\em Finite Type Invariants of W-Knotted Objects IV: Some Computations},
  paper and related files at
  \url{http://drorbn.net/AcademicPensieve/Projects/WKO4}, 
  \arXiv{1511.05624}. \backrefprint

\bibitem[BD1]{WKO1} D.~Bar-Natan and Z.~Dancso,
  \href
    {http://drorbn.net/AcademicPensieve/Projects/WKO1}
    {{\em Finite Type Invariants of W-Knotted Objects I: W-Knots and the
      Alexander Polynomial,}}
  Alg.\ and Geom.\ Top.\ {\bf 16-2} (2016) 1063--1133,
  \arXiv{1405.1956}. \backrefprint

\bibitem[BD2]{WKO2} D.~Bar-Natan and Z.~Dancso,
  \href
    {http://drorbn.net/AcademicPensieve/Projects/WKO2}
    {{\em Finite Type Invariants of W-Knotted Objects II: Tangles and
      the Kashiwara-Vergne Problem,}}
  Math.\ Ann.\ {\bf 367} (2017) 1517--1586, \arXiv{1405.1955}. \backrefprint

\bibitem[BD3]{WKO3} D.~Bar-Natan and Z.~Dancso,
  {\em Finite Type Invariants of W-Knotted Objects III: Double Tree Construction,}
  \url{http://drorbn.net/AcademicPensieve/Projects/WKO3} (in preparation).
  \backrefprint

\bibitem[BDV]{Self} D.~Bar-Natan, Z.~Dancso, and R.~van der Veen,
  {\em Over then Under Tangles,}
  (self-reference), paper and related files at
  \url{http://drorbn.net/OU-JKTR}. The \arXiv{2007.09828} edition may be older. \backrefprint

\bibitem[BM]{Bar-NatanMorrison:KnotTheory} D.~Bar-Natan, S.~Morrison, and others,
  {\tt KnotThery`}, a knot theory mathematica package,
  \url{http://katlas.org/wiki/The_Mathematica_Package_KnotTheory}. \backrefprint

\bibitem[BCP]{BellingeriCisnerosParis:WordProblem} P.~Bellingeri,
  B.~A.~Cisneros de la Cruz, and L.~Paris,
  {\em A Simple Solution to the Word Problem for Virtual Braid Groups,}
  Pac.\ J.\ of Math.\ {\bf 283-2} (2016) 271--287, \arXiv{1506.05283}. \backrefprint

\bibitem[Be]{Bergman:Diamond} G.~M.~Bergman,
  {\em The Diamond Lemma for Ring Theory,}
  Adv.\ in Math.\ {\bf 29-2} (1978) 178--218. \backrefprint

\bibitem[BB]{BirmanBrendle:BraidsSurvey} J.~S.~Birman and T.~E.~Brendle,
  {\em Braids: A Survey,}
  in {\em Handbook of Knot Theory,} (W.~Menasco, M.~Thistlethwaite, eds.) Elsevier 2005, \arXiv{math/0409205}.
  \backrefprint

\bibitem[Ch1]{Chterental:VBandVCD} O.~Chterental,
  {\em Virtual Braids and Virtual Curve Diagrams,}
  J.\ of Knot Theory and its Ramifications {\bf 24-13} (2015), \arXiv{1411.6313}. \backrefprint

\bibitem[Ch2]{Chterental:Thesis} O.~Chterental,
  {\em Virtual Braids and Virtual Curve Diagrams,}
  University of Toronto Ph.D.\ thesis, \url{http://hdl.handle.net/1807/70904}. \backrefprint

\bibitem[En1]{Enriquez:UniversalAlgebras} B.~Enriquez,
  {\em On Some Universal Algebras Associated to the Category of Lie Bialgebras,}
  Adv.\ in Math.\ {\bf 164-1} (2001) 1--23, \arXiv{math/0101059}. \backrefprint

\bibitem[En2]{Enriquez:QuantizationFunctors} B.~Enriquez,
  {\em A Cohomological Construction of Quantization Functors of Lie Bialgebras,}
  Adv.\ in Math.\ {\bf 197-2} (2005) 430--479, \arXiv{math/0212325}. \backrefprint

\bibitem[Ep]{Epstein:WordProcessing} D.~B.~A.~Epstein and others,
  {\em Word Processing in Groups,}
  A.~K.~Peters, Natick, 1992. \backrefprint

\bibitem[EK]{EtingofKazhdan:BialgebrasI} P.~Etingof and D.~Kazhdan,
  {\em Quantization of Lie Bialgebras, I,}
  Sel.\ Math.\ New Series {\bf 2} (1996) 1--41,
  \arXiv{q-alg/9506005}. \backrefprint

\bibitem[GP]{GodelleParis:WordProblems} E.~Godelle and L.~Paris,
  {\em $K(\pi,1)$ and Word Problems for Infinite Type Artin-Tits Groups, and Applications to
    Virtual Braid Groups,}
  Math.\ Zeitschrift {\bf 272} (2010) 1339–-1364, \arXiv{1007.1365}. \backrefprint

\bibitem[Ka1]{Kauffman:VirtualKnotTheory} L.~H.~Kauffman,
  {\em Virtual Knot Theory,}
  European J.\ Comb.\ {\bf 20} (1999) 663--690, \arXiv{math.GT/9811028}.
  \backrefprint

\bibitem[Ka2]{Kauffman:RotationalVirtualKnots} L.~H.~Kauffman,
  {\em Rotational Virtual Knots and Quantum Link Invariants,}
  \arXiv{1509.00578}. \backrefprint

\bibitem[Ma]{Manturov:VirtualKnots} V.~O.~Manturov,
  {\em Virtual Knots, The State of the Art,}
  Series on Knots and Everything {\bf 51}, World Scientific 2012. \backrefprint

\bibitem[Mi]{Milnor:LinkGroups} J.~W. Milnor,
  {\em Link Groups,}
  Annals of Math.\ {\bf 59} (1954) 177--195. \backrefprint

\bibitem[MV]{MurakamiVanDerVeen:Quantized} J.~Murakami and R.~van~der~Veen,
  {\em Quantized $SL(2)$ Representations of Knot Groups,}
  \arXiv{1812.09539}. \backrefprint

\bibitem[Ne]{Newman:DiamondLemma} M.~H.~A.~Newman,
  {\em On Theories with a Combinatorial Definition of ``Equivalence'',}
  Ann.\ of Math.\ 2nd Ser.\ {\bf 43-2} (1942) 223--243. \backrefprint

\bibitem[Sa]{Sapir:CombinatorialAlgebra} M.~V.~Sapir,
  {\em Combinatorial Algebra: Syntax and Semantics,}
  Springer 2014. \backrefprint

\bibitem[Se]{Severa:BialgebrasRevisited} P.~\v{S}evera,
  {\em Quantization of Lie Bialgebras Revisited,}
  Sel.\ Math.\ New Series {\bf 22} (2016) 1563--1581, \arXiv{1401.6164}. \backrefprint

\bibitem[Sm]{Smolka:Confluence} G.~Smolka,
  {\em Confluence and Normalization in Reduction Systems,}
  Lecture Notes, 2015, \url{https://www.ps.uni-saarland.de/courses/sem-ws15/ars.pdf}.
  \backrefprint

\bibitem[Th]{ThurstonD:Sutured} D.~Thurston,
  {Sutured Manifolds and Hopf algebras,}
  talk
  at \href{http://drorbn.net/m19}{\em Expansions, Lie Algebras,
  and Invariants,} Workshop at CRM, Montreal, July 2019. Video at
  \url{http://drorbn.net/m19/#Thurston}. \backrefprint

\bibitem[Wol]{Wolfram:Mathematica} 
  {\em Wolfram Language \& System Documentation Center,}
  \web{Wolf}. \backrefprint

\bibitem[Wor]{Woronowicz:Solutions} S.~L.~Woronowicz,
  {\em Solutions of the Braid Equations Related to a Hopf Algebra,}
  Lett.\ Math.\ Phys.\ {\bf 23} (1991) 143--145. \backrefprint

\end{thebibliography}
