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A twisted dimer model for knots

Moshe Cohen;  Oliver T. Dasbach;  Heather M. Russell — 2014

Fundamenta Mathematicae

We develop a dimer model for the Alexander polynomial of a knot. This recovers Kauffman's state sum model for the Alexander polynomial using the language of dimers. By providing some additional structure we are able to extend this model to give a state sum formula for the twisted Alexander polynomial of a knot depending on a representation of the knot group.

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