An introduction to Thompson knot theory and to Jones subgroups

TL;DR

This paper reviews Vaughan Jones's construction of knots from Thompson groups, exploring both oriented and unoriented versions, and introduces key concepts in Thompson knot theory.

Contribution

It provides an accessible introduction to Thompson knot theory and the Jones subgroups, highlighting their construction and significance.

Findings

Connection between Thompson groups and knot theory established

Introduction of Jones subgroups within Thompson groups

Framework for constructing knots from Thompson group elements

Abstract

We review a constructions of knots from elements of the Thompson groups due to Vaughan Jones, which comes in two flavours: oriented and unoriented.