\documentclass[10pt,leqno]{ws-jktr}
\def\draft{n}
\usepackage{
  graphicx, dbnsymb, amsmath, amssymb, multicol, mathtools,
  picins, stmaryrd, xcolor, mathabx, needspace, enumitem,
  lgreek, sidecap, mathbbol, blindtext, bigfoot, import, amscd
}
\usepackage[all]{xy}
%\usepackage[english,greek]{babel}
%\usepackage{printlen} % Used to print lengths.

% Following http://tex.stackexchange.com/a/847/22475:
\usepackage[pagebackref,breaklinks=true]{hyperref}\hypersetup{colorlinks,
  linkcolor={green!50!black},
  citecolor={green!50!black},
  urlcolor=blue
}

%\usepackage{caption} \captionsetup{textfont=sf,width=5.5in}

\if\draft y
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\fi

\input defs.tex

\interfootnotelinepenalty=10000 % prevent footnotes from extending across pages.

\begin{document} %\latintext
%\newdimen\captionwidth\captionwidth=\hsize
\setcounter{secnumdepth}{4}
\raggedbottom

%\noindent {\bf JKTR Conversion Comments.}
%\begin{enumerate}
%\item I had to comment out the \verb$\tableofcontent$ line as \verb$ws-jktr.cls$ does not seem to support
%  it. I hope it can be returned!
%\end{enumerate}
%\newpage

\title{Over then Under Tangles}

\author{Dror~Bar-Natan}
\address{
  Department of Mathematics\\
  University of Toronto\\
  Toronto Ontario M5S 2E4, Canada \\
  \href{mailto:drorbn@math.toronto.edu}{drorbn@math.toronto.edu}
  and \url{http://www.math.toronto.edu/drorbn}
}

\author{Zsuzsanna Dancso}
\address{
  School of Mathematics and Statistics\\
  The University of Sydney\\
  Eastern Ave, Camperdown NSW 2006, Australia \\
  \href{mailto:zsuzsanna.dancso@sydney.edu.au}{zsuzsanna.dancso@sydney.edu.au}
  and \url{http://zsuzsannadancso.net}
}

\author{Roland~van~der~Veen}
\address{
  University of Groningen, Bernoulli Institute\\
  P.O. Box 407\\
  9700 AK Groningen, The Netherlands\\
  \href{mailto:roland.mathematics@gmail.com}{roland.mathematics@gmail.com}
  and \url{http://www.rolandvdv.nl/}
}

\maketitle

\begin{abstract} {\def\me{}
  \input abstract.tex

  \vskip 3mm
  \noindent{\em Online versions:} \cite{Self}.
}\end{abstract}

\keywords{knots, braids, virtual braids, tangles, virtual tangles, diamond lemma, extraction graphs, Drinfel'd double}

\ccode{Mathematics Subject Classification 2020: 57K12, 20F36, 20F38}

\setcounter{tocdepth}{3}
%\tableofcontents


\draftcut \input{f.tex}

\draftcut \input{c.tex}

\draftcut \input{v.tex}

\draftcut \input{a.tex}

\draftcut \input{SomeComputations.tex}

\draftcut \input{m.tex}

\draftcut \section{Acknowledgement} We wish to thank P.~Bellingeri,
A.~Referees, D.~Thurston, and B.~Wiest for comments and suggestions,
and especially O.~Chterental for spotting a major gap in an earlier
version of this paper. This work was partially supported by NSERC grant
RGPIN-2018-04350, by the University of Sydney Visiting Scholar Scheme,
and by the Chu Family Foundation (NYC).

\input refs.tex

%\draftcut
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\end{document}
\endinput

