Related papers: Positive oriented Thompson links
We show that the links associated with positive elements of the Thompson group $F$ coincide with the closures of bipartite arborescent tangles.
We define half grid diagrams and prove every link is half grid presentable by constructing a canonical half grid pair (which gives rise to a grid diagram of some special type) associated with an element in the oriented Thompson group. We…
We show how to construct unitary representations of the oriented Thompson group $\vec{F}$ from oriented link invariants. In particular we show that the suitably normalised HOMFLYPT polynomial defines a positive definite function of…
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 review recent developments in the theory of Thompson group representations related to knot theory.
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,…
We extend a construction of Jones to associate $(n, n)$-tangles with elements of Thompson's group $F$ and prove that it is asymptotically faithful as $n \to\infty$. Using this construction we show that the oriented Thompson group $\vec F$…
We review a constructions of knots from elements of the Thompson groups due to Vaughan Jones, which comes in two flavours: oriented and unoriented.
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 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"…
We prove that the solvable radical of a finite group G coincides with the set of elements y having the following property: for any x in G the subgroup of G generated by x and y is solvable. We present analogues of this result for finite…
We prove that R. Thompson groups F, T, V have linear divergence functions.
We show that the density of elements in Thompson's groups T and V which have north-south dynamics acting on the circle is positive with respect to a stratification in terms of size. We show that the fraction of element pairs which generate…
We give a new proof of the Mordell-Lang conjecture in positive characteristic for finitely generated subgroups. We also make some progress towards the full Mordell-Lang conjecture in positive characteristic.
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…
In [Jo14] and [Jo18] Vaughan Jones introduced a construction which yields oriented knots and links from elements of the oriented Thompson group $\vec{F}$. In this paper we prove, by analogy with Alexander's classical theorem establishing…
We give a simple combinatorial proof that the rotation number for each element in Thompson's group ${\bf T}$ is rational.
In 2014, Vaughan Jones developed a method to produce links from elements of Thompson's group $F$, and showed that all links arise this way. He also introduced a subgroup $\vec{F}$ of $F$ and a method to produce oriented links from elements…
We show that pure subgroups of infinitely braided Thompson's are bi-orderable. For every finitely generated pure subgroup, we give explicit sets of generators.
We prove some necessary conditions for a link to be either concordant to a quasi-positive link, quasi-positive, positive, or the closure of a positive braid. The main applications of our results are a characterisation of positive links with…