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\begin{document}
\title[Meta-Monoids]{Meta-Monoids, Meta-Bicrossed Products, 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{Sam Selmani}
\address{
McGill University\\
Department of Physics\\
Montreal, Quebec H3A 2T8\\
Canada
}
\email{sam.selmani@physics.mcgill.ca}
\date{\today; first edition: February 19, 2013. Published at {\em Journal of Knot Theory and its Ramifications {\bf 22-10} (2013)}}
\keywords{Meta-monoids, Meta-groups, Bicrossed products, Alexander polynomial}
\subjclass{57M25}
\thanks{This work was partially supported by NSERC grant RGPIN 262178 and partially pursued at the Newton Institute in Cambridge, UK. The full \TeX\ sources are at \url{http://drorbn.net/AcademicPensieve/Projects/MetaMonoids/}. This is \arXiv{1302.5689}.}
\maketitle
\begin{abstract}
We introduce a new invariant of tangles along with an algebraic framework in which to understand it. We claim that the invariant contains the classical Alexander polynomial of knots and its multivariable extension to links. We argue that of the computationally efficient members of the family of Alexander invariants, it is the most meaningful.
These are lecture notes for talks given by the first author, written and completed by the second. The talks, with handouts and videos, are available at \url{http://www.math.toronto.edu/drorbn/Talks/Regina-1206/}. See also further comments at \url{http://www.math.toronto.edu/drorbn/Talks/Caen-1206/#June8}.
\end{abstract}
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