# On normal subgroups of the braided Thompson groups.

@article{Zaremsky2014OnNS, title={On normal subgroups of the braided Thompson groups.}, author={Matthew C. B. Zaremsky}, journal={arXiv: Group Theory}, year={2014} }

We inspect the normal subgroup structure of the braided Thompson groups Vbr and Fbr. We prove that every proper normal subgroup of Vbr lies in the kernel of the natural quotient Vbr \onto V, and we exhibit some families of interesting such normal subgroups. For Fbr, we prove that for any normal subgroup N of Fbr, either N is contained in the kernel of Fbr \onto F, or else N contains [Fbr,Fbr]. We also compute the Bieri-Neumann-Strebel invariant Sigma^1(Fbr), which is a useful tool for…

## 9 Citations

### Thompson-like groups, Reidemeister numbers, and fixed points

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. We investigate ﬁxed-point properties of automorphisms of groups similar to R. Thompson’s group F . Revisiting work of Gon¸calves–Kochloukova, we deduce a cohomological criterion to detect inﬁnite…

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We study quasimorphisms and bounded cohomology of a variety of braided ver-sions of Thompson groups. Our ﬁrst main result is that the Brin–Dehornoy braided Thompson group bV has an…

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We calculate the Bieri-Neumann-Strebel-Renz invariant $\Sigma^1(G)$ for even Artin groups $G$ with underlying graph $\Gamma$ such that if there is a closed reduced path in $\Gamma$ with all labels…

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. Golan and Sapir proved that Thompson’s groups F , T and V have linear divergence. In the current paper, we focus on the divergence property of several generalisations of the Thompson groups. We…

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We study the Newton polytopes of determinants of square matrices defined over rings of twisted Laurent polynomials. We prove that such Newton polytopes are single polytopes (rather than formal…

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We study the group $QV$, the self-maps of the infinite $2$-edge coloured binary tree which preserve the edge and colour relations at cofinitely many locations. We introduce related groups $QF$, $QT$,…

### Geometric structures related to the braided Thompson groups

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In previous work, joint with Bux, Fluch, Marschler and Witzel, we proved that the braided Thompson groups are of type F∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym}…

### Von Neumann algebras of Thompson-like groups from cloning systems

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We prove a variety of results about the group von Neumann algebras associated to Thompson-like groups arising from so called $d$-ary cloning systems. Cloning systems are a framework developed by…

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