On Jones' connections between subfactors, conformal field theory, Thompson's groups and knots

Abstract

Surprisingly Richard Thompson's groups have recently appeared in Jones' subfactor theory. Vaughan Jones is famous for linking theories that are a priori completely disconnected; for instance, his celebrated polynomial for links emanating from subfactor theory. This note is about a new beautiful story in mathematics which results from a fortunate accident in the land of quantum field theory.

References in corpus (12)

• Noncommutative Manifolds the Instanton Algebra and Isospectral Deformations
• Planar algebras, I
• The chameleon groups of Richard J. Thompson: automorphisms and dynamics
• The classification of subfactors of index at most 5
• The Algebra of Strand Splitting. I. A Braided Version of Thompson's Group V
• Operator-algebraic construction of gauge theories and Jones' actions of Thompson's groups
• The Homflypt polynomial and the oriented Thompson group
• Jones representations of Thompson's group $F$ arising from Temperley-Lieb-Jones algebras
• Continuum limits of homogeneous binary trees and the Thompson group
• Canonical quantization of 1+1-dimensional Yang-Mills theory: An operator-algebraic approach
• Quantum fields for unitary representations of Thompson's groups F and T
• On Jones Subgroup of R. Thompson's Group $T$