# Classification of Thompson related groups arising from Jones technology I

@article{Brothier2020ClassificationOT, title={Classification of Thompson related groups arising from Jones technology I}, author={Arnaud Brothier}, journal={arXiv: Group Theory}, year={2020} }

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 framework for constructing actions of particular groups arising from categories such as Richard Thompson's groups and braid groups. In particular, given a group and two of its endomorphisms one can construct a semidirect product. Those semidirect products have remarkable diagrammatic descriptions which…

## 2 Citations

Braiding groups of automorphisms and almost-automorphisms of trees

- Mathematics
- 2021

We introduce “braided” versions of self-similar groups and Röver–Nekrashevych groups, and study their finiteness properties. This generalizes work of Aroca and Cumplido, and the first author and Wu,…

## References

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- 2021

We prove irreducibility and mutual inequivalence for certain unitary representations of R. Thompson's groups F and T.

On closed subgroups of the R. Thompson group $F$.

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- 2021

We prove that Thompson's group $F$ has a subgroup $H$ such that the conjugacy problem in $H$ is undecidable and the membership problem in $H$ is easily decidable. The subgroup $H$ of $F$ is a closed…

Classification of thompson related groups arising from Jones technology I

- 2020

On the Alexander theorem for the oriented
Thompson group F

- MathematicsAlgebraic & Geometric Topology
- 2020

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…

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- 2019

Using recent techniques introduced by Jones we prove that a large family of discrete groups and groupoids have the Haagerup property. In particular, we show that if G is a discrete group with the…

Jones Representations of Thompson’s Group F Arising from Temperley–Lieb–Jones Algebras

- MathematicsInternational Mathematics Research Notices
- 2019

Following a procedure due to Jones, using suitably normalized elements in a Temperley–Lieb–Jones (planar) algebra, we introduce a 3-parametric family of unitary representations of the Thompson’s…

On Jones' connections between subfactors, conformal field theory, Thompson's groups and knots

- Mathematics
- 2019

Surprisingly Richard Thompson's groups have recently appeared in Jones' subfactor theory. Vaughan Jones is famous for linking theories that are a priori completely disconnected; for instance, his…

On Jones’ connections between subfactors

- conformal field theory, Thompson’s groups and knots. to appear in Celebratio Mathematica, Preprint
- 2019

On the Construction of Knots and Links from Thompson’s Groups

- MathematicsKnots, Low-Dimensional Topology and Applications
- 2019

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