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\begin{document} %\latintext
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\title{Poly-Time Knot Polynomials Via Solvable Approximations}

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

\author{Roland~van~der~Veen}
\address{
  Mathematisch Instituut\\
  Universiteit Leiden\\
  Niels Bohrweg 1\\
  2333 CA Leiden\\
  The Netherlands
}
\email{roland.mathematics@gmail.com}
\urladdr{http://www.rolandvdv.nl/}

\date{First edition Not Yet, 2017, this edition Oct.~24,~2017.}

\subjclass[2010]{57M25}
\keywords{
  knots,
  tangles,
  knot polynomials,
  Lie algebras,
  Lie bialgebras,
  quantization,
  2-parameter quantum groups,
  Drinfel'd double}

\thanks{This work was partially supported by NSERC grant RGPIN 262178.}

\begin{abstract}
  \input abstract.tex

  \vskip 6mm\noindent
  Electronic version, links, and related files at \web{}$\coloneqq$\url{\weburl/}.
\end{abstract}

\maketitle

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\draftcut\input intro.tex

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%\section{The First Example: Only the Algorithm, Only for Knots} {\red MORE.}

\section{Rotational Virtual Tangles} \label{sec:RVT}
(This section can be read independently of the rest of this paper).

{\red More.}

\section{The Zeroth Example in Detail} {\red MORE.}

\section{The Lie Algebra $sl_2^{\alpha,\beta}$ and its Quantization} {\red MORE.}
(This section can be read independently of the rest of this paper).

\section{Computations in (Quantized) Enveloping Algebras: Trading Non-Commutativity for Non-Linearity}
(This section can be read independently of the rest of this paper).

{\red More.}

\section{Pushforwards of Pure Distributions}
(This section can be read independently of the rest of this paper).

{\red Content: Pushforwards in general, interpretation using pairings,
the difficulty in the general case, central-nilpotent-diagonal and the
main theorem.}

{\red More.}

\section{The General $sl_2^{\leq k}$ Invariant} {\red MORE.}

\section{Bulk Stitching} {\red MORE.}

\section{Behaviour under strand reversal and strand doubling} \label{sec:ops} {\red
MORE.}

\section{Complexity} {\red MORE.}

\section{Experimental Results} {\red MORE.}

\draftcut\input{odds.tex}

\section{Tables} {\red MORE.}

\draftcut\input refs.tex

\draftcut\input recycling.tex

\parpic[l]{\includegraphics[height=2in]{WordCloud.png}}


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