Approximating nonabelian free groups by groups of homeomorphisms of the real line
| Autor: | Yash Lodha |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
left orderable
Group Theory (math.GR) Type (model theory) Rank (differential topology) 01 natural sciences torsion free Combinatorics Mathematics::Group Theory 0103 physical sciences FOS: Mathematics Golden ratio 0101 mathematics Real line Mathematics Sequence Algebra and Number Theory piecewise Group (mathematics) 010102 general mathematics space 16. Peace & justice Orientation (vector space) space of marked groups free group Free group projective 010307 mathematical physics Mathematics - Group Theory |
| DOI: | 10.48550/arxiv.2001.05413 |
| Popis: | We show that for a large class $\mathcal{C}$ of finitely generated groups of orientation preserving homeomorphisms of the real line, the following holds: Given a group $G$ of rank $k$ in $\mathcal{C}$, there is a sequence of $k$-markings $(G, S_n), n\in \mathbf{N}$ whose limit in the space of marked groups is the free group of rank $k$ with the standard marking. The class we consider consists of groups that admit actions satisfying mild dynamical conditions and a certain "self-similarity" type hypothesis. Examples include Thompson's group $F$, Higman-Thompson groups, Stein-Thompson groups, various Bieri-Strebel groups, the golden ratio Thompson group, and finitely presented non amenable groups of piecewise projective homeomorphisms. For the case of Thompson's group $F$ we provide a new and considerably simpler proof of this fact proved by Brin (Groups, Geometry, and Dynamics 2010). Comment: 8 pages. Referee comments incorporated: to appear in the Journal of Algebra |
| Databáze: | OpenAIRE |
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