A twisted dimer model for knots
Volume 225 / 2014
Fundamenta Mathematicae 225 (2014), 57-74
MSC: 57M25, 57M27, 05C50, 05C70.
DOI: 10.4064/fm225-1-4
Abstract
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.
