Divergence properties of the generalised Thompson groups and the braided-Thompson groups

Xiaobing Sheng

Divergence properties of the generalised Thompson groups and the braided-Thompson groups

Group Theory 2022-09-27 v2

Authors: Xiaobing Sheng

Abstract

Golan and Sapir \cite{MR3978542} proved that the Thompson's groups $F$ , $T$ and $V$ have linear divergence. In the current paper, we focus on the divergence properties of several generalisation of the Thompson's groups, we first consider the Brown-Thompson's groups $F_n$ , $T_n$ and $V_n$ and found out that these groups also have linear divergence function. We then consider the braided Thompson's groups $BF$ and $\widehat{BF}$ and $\widehat{BV}$ together with the result in \cite{Kodama:2020to} we conclude that theses groups have linear divergence.

Keywords

thompson groups generalised thompson groups braided-thompson groups divergence linear divergence brown-thompson groups

Cite

@article{arxiv.2106.15571,
  title  = {Divergence properties of the generalised Thompson groups and the braided-Thompson groups},
  author = {Xiaobing Sheng},
  journal= {arXiv preprint arXiv:2106.15571},
  year   = {2022}
}

Comments

29 pages, 10 figures, Major revisions on Lemma 3.6, Corollary 3.7, the proof of Proposition 3.9, lemma 4.9, lemma 4.10, lemma 4.12, lemma 4.17 and proposition 4.19 made. Minor errors corrected. Suggestions and comments are welcome!

Divergence properties of the generalised Thompson groups and the braided-Thompson groups

Abstract

Keywords

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