相关论文: Classification of Thompson related groups arising …

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…

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…

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…

Hughes has defined a class of groups, which we call FSS (finite similarity structure) groups. Each FSS group acts on a compact ultrametric space by local similarities. The best-known example is Thompson's group V. Guided by previous work on…

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

There is a map, defined and studied by Jones, from Thompson's group $F$ to knots. Jones proved that every knot is in the image of this map -- that is, that every knot can be seen as the "knot closure" of a Thompson group element. We…

We review recent developments in the theory of Thompson group representations related to knot theory.

Tree tensor network descriptions of critical quantum spin chains are empirically known to reproduce correlation functions matching CFT predictions in the continuum limit. It is natural to seek a more complete correspondence, additionally…

We prove that the braided Thompson's groups $V_{\rm br}$ and $F_{\rm br}$ are of type $F_\infty$, confirming a conjecture by John Meier. The proof involves showing that matching complexes of arcs on surfaces are highly connected. In an…

We introduce Thompson field theory, a class of toy models of conformal field theory in which Thompson's group T takes the role of a discrete analogue of the chiral conformal group. T and the related group F are discrete transformations of…

Hughes defined a class of groups that act as local similarities on compact ultrametric spaces. Guba and Sapir had previously defined braided diagram groups over semigroup presentations. The two classes of groups share some common…

We describe a procedure for constructing a generalized Thompson group out of a family of groups that is equipped with what we call a cloning system. The previously known Thompson groups F, V, Vbr and Fbr arise from this procedure using,…

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,…

The authors continue a series of articles studying certain unitary representations of the Richard Thompson groups $F,T,V$ called Pythagorean. They all extend to the Cuntz algebra $\mathcal{O}$ and conversely all representations of…

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 previous work, joint with Bux, Fluch, Marschler and Witzel, we proved that the braided Thompson groups are of type $\textrm{F}_\infty$. The proof utilized certain contractible cube complexes, which in this paper we prove are CAT(0). We…

We describe standard forms for elements of the higher-dimensional Thompson groups $nV$ arising from gridding subdivision processes. These processes lead to standard normal form descriptions for elements in these groups, and sizes of these…

We demonstrate the existence of a family of finitely generated subgroups of Richard Thompson's group $F$ which is strictly well-ordered by the embeddability relation in type $\epsilon_0 +1$. All except the maximum element of this family…

For virtual knot theory, the virtual braid group was defined by generalizing the braid group. It was proved that any virtual link can be obtained by the closure of a virtual braid. On the other hand, due to work by Jones et al., it is known…

Almost-direct products of free groups arise naturally in braid theory and in the study of automorphism groups of free groups. Although bi-invariant orderings are known to exist for many such groups, their explicit structure is often left…