We prove that the free group F2 admits a faithful discrete representation into Diff+1[0,1]. We also prove that F2 admits a faithful discrete representation of bi-Lipschitz class into Homeo+[0,1]. Some properties of these representations are studied.
Akhmedov, Azer  1
@article{10_2140_agt_2010_10_2409,
author = {Akhmedov, Azer},
title = {On free discrete subgroups of {Diff(I)}},
journal = {Algebraic and Geometric Topology},
pages = {2409--2418},
year = {2010},
volume = {10},
number = {4},
doi = {10.2140/agt.2010.10.2409},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2010.10.2409/}
}
Akhmedov, Azer. On free discrete subgroups of Diff(I). Algebraic and Geometric Topology, Tome 10 (2010) no. 4, pp. 2409-2418. doi: 10.2140/agt.2010.10.2409
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