A twisted dimer model for knots
Moshe Cohen, Oliver T. Dasbach, Heather M. Russell
TL;DR
This paper introduces a dimer model for the Alexander polynomial of knots, extending it to twisted Alexander polynomials via additional structure, connecting knot invariants with statistical mechanics models.
Contribution
It develops a novel dimer model framework for knot invariants, unifying and extending Kauffman's state sum model to twisted Alexander polynomials.
Findings
Dimer model recovers Kauffman's state sum for Alexander polynomial
Extended model provides a state sum formula for twisted Alexander polynomial
Connects knot invariants with statistical mechanics models
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.
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