Tame combings and easy groups
type: Item
instance of: scholarly article
title: Tame combings and easy groups
zbMATH Open document ID: 1412.57014
author: Daniele Ettore Otera
author: Valentin Poénaru
published in: Forum Mathematicum
publication date: 2017-05-03T00:00:00Z
review text: Let $G$ be a finitely presented group and $\mathcal{G}$ its Cayley graph. A $ 0$-combing for $G$ is defined by the following: for any $g\in G,$ there exists a polygonal path $\gamma_{g}(t)\subset \mathcal{G}$, $t\in [a,b],$ such that $\gamma_{g}(0)=id\in G$ and $\gamma_{g}(1)=g.$ The combing is called tame if for any $n$-ball $B_{n}$ in $\mathcal{G}$ there is a connected subset $D_{n}$ containing $B_{n}$ such that for any $g\in G,$ the intersection $\gamma_{g}\cap B_{n}$ is contained in the connected component of $\gamma_{g}\cap D_{n}$ with identity $id\in G.$ Moreover, a $0$-combing is Lipschitz if there exist constants $C_{1},C_{2}>0$ such that for any $ g_{1},g_{2}\in G$ we have \[ d(\gamma_{g_{1}}(t),\gamma_{g_{2}}(t))\leq C_{1}d(g_{1},g_{2})+C_{2}. \] The main result of the article under review is that if a finitely presented group admits a Lipschitz and tame 0-combing, then it is easy and hence QSF (quasi-simply filtered).
Mathematics Subject Classification ID: 57N35
zbMATH DE Number: 6710808
zbMATH Keywords: combings
zbMATH Keywords: quasi-simple filtration (QSF)
zbMATH Keywords: inverse representations
zbMATH Keywords: easy groups
reviewed by: Shengkui Ye
MaRDI profile type: Publication
full work available at URL: forum-2015-0063
OpenAlex ID: W2507325971
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DOI: 10.1515/FORUM-2015-0063
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description: scientific article; zbMATH DE number 6710808