Jones Index Theorem revisited

TL;DR

This paper offers a new proof of the Jones Index Theorem by utilizing K-theory of a specific cluster C*-algebra associated with the Riemann sphere, providing fresh insights into operator algebra theory.

Contribution

It presents a novel proof of the Jones Index Theorem through K-theory of a cluster C*-algebra, connecting operator algebras with geometric structures.

Findings

Proof of Jones Index Theorem via K-theory

Establishes a link between cluster C*-algebras and operator algebra invariants

Provides a new perspective on the algebraic structure of the Riemann sphere

Abstract

We prove the Jones Index Theorem using the K-theory of a cluster $C^*$-algebra of the Riemann sphere with two boundary components.