On knot invariants related to some statistical mechanical models

Abstract

We use three different kinds of statistical mechanical models to construct link invariants. The vertex models emerge as the most general. Our treatment of them is essentially the same as Turaev’s. Using the work of Goldschmidt we are able to define models whose invariants are homology invariants for branched covers. Thus the statistical mechanical framework embraces both the "classical" and the "new" link invariants. © 1989 by Pacific Journal of Mathematics.