#### Volume 10, issue 4 (2010)

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1472-2739 ISSN (print): 1472-2747
On free discrete subgroups of $\mathrm{Diff}(I)$

### Azer Akhmedov

Algebraic & Geometric Topology 10 (2010) 2409–2418
##### Abstract

We prove that the free group ${\mathbb{F}}_{2}$ admits a faithful discrete representation into ${Diff}_{+}^{1}\left[0,1\right]$. We also prove that ${\mathbb{F}}_{2}$ admits a faithful discrete representation of bi-Lipschitz class into ${Homeo}_{+}\left[0,1\right]$. Some properties of these representations are studied.

##### Keywords
diffeomorphisms of the interval, discrete representation, free groups
Primary: 37E05
Secondary: 20F65