Three-Dimensional Integrable Models and Associated Tangle Invariants

TL;DR

This paper demonstrates how certain three-dimensional integrable models yield braid group representations and link invariants through spectral limits, expanding the understanding of topological invariants in mathematical physics.

Contribution

It classifies spectral limits of the Baxter-Bazhanov model that produce braid group representations and introduces new tangle invariants generalizing cyclotomic invariants.

Findings

Spectral limits produce braid group representations

Some limits yield cyclotomic link invariants

Other limits generate generalized tangle invariants

Abstract

In this paper we show that the Boltzmann weights of the three-dimensional Baxter-Bazhanov model give representations of the braid group, if some suitable spectral limits are taken. In the trigonometric case we classify all possible spectral limits which produce braid group representations. Furthermore we prove that for some of them we get cyclotomic invariants of links and for others we obtain tangle invariants generalizing the cyclotomic ones.