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A twisted dimer model for knots

Tom 225 / 2014

Moshe Cohen, Oliver T. Dasbach, Heather M. Russell Fundamenta Mathematicae 225 (2014), 57-74 MSC: 57M25, 57M27, 05C50, 05C70. DOI: 10.4064/fm225-1-4

Streszczenie

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.

Autorzy

  • Moshe CohenDepartment of Mathematics
    Technion – Israel Institute of Technology
    Haifa, 32000 Israel
    e-mail
  • Oliver T. DasbachDepartment of Mathematics
    Louisiana State University
    Baton Rouge, LA 70803, U.S.A.
    e-mail
  • Heather M. RussellDepartment of Mathematics and Computer Science
    Washington College
    Chestertown, MD 21620, U.S.A.
    e-mail

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