Volume 10, issue 4 (2010)

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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