A state model for the multi-variable alexander polynomial

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Abstract

We construct a vertex type state model in Turaev’s sense for the multi-variable (non-reduced) Alexander polynomial. Our model is a colored version of the 6-vertex free fermion model. To show the correspondence of our model and the multi-variable Alexander polynomial, we introduce colored braid groups and their Magnus representations. By using this model, a new set of axioms for the multi-variable Alexander polynomial is obtained.

Original languageEnglish
Pages (from-to)109-135
Number of pages27
JournalPacific Journal of Mathematics
Volume157
Issue number1
Publication statusPublished - 1993
Externally publishedYes

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ASJC Scopus subject areas

  • Mathematics(all)

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