On free discrete subgroups of Diff(I)

Akhmedov, Azer

doi:10.2140/agt.2010.10.2409

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On free discrete subgroups of $\mathrm{Diff}(I)$

Azer Akhmedov

Algebraic & Geometric Topology 10 (2010) 2409–2418

DOI: 10.2140/agt.2010.10.2409

Abstract

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

Keywords

diffeomorphisms of the interval, discrete representation, free groups

Mathematical Subject Classification 2000

Primary: 37E05

Secondary: 20F65

References

Publication

Received: 26 April 2010

Revised: 14 September 2010

Accepted: 15 September 2010

Published: 19 December 2010

Authors

Azer Akhmedov
Department of Mathematics North Dakota State University Fargo ND 58102 USA

Volume 10, issue 4 (2010)