# The Alexander Polynomial of a Knotted Trivalent Graph

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Statement. The Alexander polynomial of a knotted trivalent graph $\gamma$ is the Reidemeister torsion of the singular homology complex of the complement of $\gamma$, with local coefficients twisted using the Alexander duality pairing with $H_1(\gamma)$. Thus is it a numerical function on $H_1(\gamma)$; in particular, if $\gamma$ is a link, it is a numerical function in as many variables as the number of components of the link. In this case it is given by a Laurant polynomial.