Related papers: On Jones' connections between subfactors, conforma…
We review a constructions of knots from elements of the Thompson groups due to Vaughan Jones, which comes in two flavours: oriented and unoriented.
This paper is a memory of the work and influence of Vaughan Jones. It is an exposition of the remarkable breakthroughs in knot theory and low dimensional topology that were catalyzed by his work. The paper recalls the inception of the Jones…
This paper surveys the long-standing connections and impact between Vaughan Jones's theory of subfactors and various topics in mathematical physics, namely statistical mechanics,quantum field theory,quantum information and two-dimensional…
Vaughan Jones discovered unexpected connections between Richard Thompson's group and subfactor theory while attempting to construct conformal field theories (in short CFT). Among other this founded Jones' technology: a powerful new method…
We analyze the connections between the mathematical theory of knots and quantum physics by addressing a number of algorithmic questions related to both knots and braid groups. Knots can be distinguished by means of `knot invariants', among…
Jones' technology, developed by Vaughan Jones during his exploration of the connections between conformal field theory and subfactors, is a powerful mechanism for generating actions of groups coming from categories, notably Richard…
The Jones polynomial and the Kauffman bracket are constructed, and their relation with knot and link theory is described. The quantum groups and tangle functor formalisms for understanding these invariants and their descendents are given.…
The pioneering work of Jones and Kauffman unveiled a fruitful relationship between statistical mechanics and knot theory. Recently, Jones introduced two subgroups $\vec{F}$ and $\vec{T}$ of the Thompson groups $F$ and $T$, respectively,…
In the quest in constructing conformal field theories (CFT) Jones has discovered a beautiful and deep connection between CFT, Richard Thompson's groups and knot theory. This led to a powerful functorial framework for constructing actions of…
We review recent developments in the theory of Thompson group representations related to knot theory.
In this second article, we continue to study classes of groups constructed from a functorial method due to Vaughan Jones. A key observation of the author shows that these groups have remarkable diagrammatic properties that can be used to…
In a recent paper Jones introduced a correspondence between elements of the Thompson group $F$ and certain graphs/links. It follows from his work that several polynomial invariants of links, such as the Kauffman bracket, can be…
In Classical Knot Theory and in the new Theory of Quantum Invariants substantial effort was directed toward the search for unknotting moves on links. We solve, in this note, several classical problems concerning unknotting moves. Our…
Almost a decade ago Vaughan Jones introduced a method to produce knots from elements of the Thompson groups $F$, which was later extended to the Brown-Thompson group $F_3$. In this article we define a way to produce permutations out of…
We propose a new gauge theory of quantum electrodynamics (QED) and quantum chromodynamics (QCD) from which we derive knot invariants such as the Jones polynomial. Our approach is inspired by the work of Witten who derived knot invariants…
I present a summary of the recent progress made in field and string theory which has led to a reformulation of quantum-group polynomial invariants for knots and links into new polynomial invariants whose coefficients can be described in…
Jones introduced a method to produce unoriented links from elements of the Thompson's group $F$, and proved that any link can be produced by this construction. In this paper, we attempt to investigate the relations between conjugacy classes…
We propose a gauge model of quantum electrodynamics (QED) and its nonabelian generalization from which we derive knot invariants such as the Jones polynomial. Our approach is inspired by the work of Witten who derived knot invariants from…
In a "naive" attempt to create algebraic quantum field theories on the circle, we obtain a family of unitary representations of Thompson's groups T and F for any subfactor. The Thompson group elements are the "local scale transformations"…
In this article we shall give an account of certain developments in knot theory which followed upon the discovery of the Jones polynomial in 1984. The focus of our account will be recent glimmerings of understanding of the topological…