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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm225-1-4,
author = {Moshe Cohen and Oliver T. Dasbach and Heather M. Russell},
title = {A twisted dimer model for knots},
journal = {Fundamenta Mathematicae},
volume = {227},
year = {2014},
pages = {57-74},
zbl = {1311.57010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm225-1-4}
}
Moshe Cohen; Oliver T. Dasbach; Heather M. Russell. A twisted dimer model for knots. Fundamenta Mathematicae, Tome 227 (2014) pp. 57-74. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm225-1-4/