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\title[Finite Type Invariants of w-Knotted Objects]{Finite Type Invariants
  of w-Knotted Objects I: w-Knots and the Alexander Polynomial}

\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{Zsuzsanna Dancso}
\address{Mathematical Sciences Institute\\
  Australian National University\\
  Canberra, ACT, 2601}
\email{zsuzsanna.dancso@anu.edu.au}
\urladdr{http://www.math.toronto.edu/zsuzsi}

\date{first edition Sep.\ 27, 2013, this edition Oct.~2,~2017. The
\arXiv{1309.7155} edition may be older}

\subjclass{57M25}
\keywords{
  virtual knots,
  w-braids,
  w-knots,
  w-tangles,
  knotted graphs,
  finite type invariants,
  Alexander polynomial,
  Kashiwara-Vergne,
  associators,
  free Lie algebras%
}

\thanks{This work was partially supported by NSERC grant RGPIN 262178.
  Electronic version, videos (wClips) and related files at~\cite{WKO},
  \url{http://www.math.toronto.edu/~drorbn/papers/WKO/}.
}

\begin{abstract}
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\input knots.tex
\input odds.tex
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