On knot invariants related to some statistical mechanical models

Vaughan Jones

Vol. 137 (1989), No. 2, 311–334

DOI: 10.2140/pjm.1989.137.311

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.

Mathematical Subject Classification 2000

Primary: 57M25

Secondary: 82A69

Milestones

Received: 15 April 1988

Published: 1 April 1989