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

2019/12/15 by Arnaud Brothier, Brothier, Arnaud · 2 citations
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #Group Theory (math.GR) #History and Overview (math.HO) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1912.07140

openalex publication_date 2019/12/15 · openalex created_date 2019/12/26 · openalex updated_date 2026/07/28

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.

Citations

• On Jones Subgroup of R. Thompson's Group T

Cited by

• Finitely presented simple groups with no piecewise projective actions
• Thompson's Group V and Virtual Link Theory

Related

• Combinatorial Knot Theory and the Jones Polynomial
• Forest-skein groups I: between Vaughan Jones' subfactors and Richard Thompson's groups
• Search for different links with the same Jones' type polynomials: Ideas from graph theory and statistical mechanics
• Classification of Thompson related groups arising from Jones technology I
• Knot and Gauge Theory