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.
Publication Source (Journal or Book title)
Cohen, M., Dasbach, O., & Russell, H. (2014). A twisted dimer model for knots. Fundamenta Mathematicae, 225 (1), 57-74. https://doi.org/10.4064/fm225-1-4