A twisted dimer model for knots

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

doi:10.4064/fm225-1-4

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arXiv · 1010.5228

A twisted dimer model for knots

Moshe Cohen·Oliver T. Dasbach·Heather M. Russell

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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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BibTeX RIS

Moshe Cohen, Oliver T. Dasbach, Heather M. Russell. 2010-10-26. A twisted dimer model for knots. https://doi.org/10.4064/fm225-1-4

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