Spin models for link polynomials, strongly regular graphs and Jaeger’s Higman-Sims model

Pierre de la Harpe

Vol. 162 (1994), No. 1, 57–96

DOI: 10.2140/pjm.1994.162.57

Abstract

We recall first some known facts on Jones and Kauffman polynomials for links, and on state models for link invariants. We give next an exposition of a recent spin model due to F. Jaeger and which involves the Higman-Sims graph. The associated invariant assigns to an oriented link the evaluation for a = −τ⁵ and z = 1 of its Kauffman polynomial in the Dubrovnik form, where τ denotes the golden ratio.

Mathematical Subject Classification 2000

Primary: 57M25

Secondary: 82B20

Milestones

Received: 15 February 1992

Revised: 15 May 1992

Published: 1 January 1994