Vol. 137, No. 2, 1989

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On knot invariants related to some statistical mechanical models

Vaughan Jones

Vol. 137 (1989), No. 2, 311–334
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
Authors
Vaughan Jones
Department of Mathematics
University of California, Berkeley
Berkeley CA 94720
United States
http://math.berkeley.edu/~vfr/