Geometry & Topology

A finitely generated, locally indicable group with no faithful action by $C^1$ diffeomorphisms of the interval

Andrés Navas

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According to Thurston’s stability theorem, every group of C1 diffeomorphisms of the closed interval is locally indicable (that is, every finitely generated subgroup factors through ). We show that, even for finitely generated groups, the converse of this statement is not true. More precisely, we show that the group F22, although locally indicable, does not embed into Diff+1((0,1)). (Here F2 is any free subgroup of SL(2,), and its action on 2 is the linear one.) Moreover, we show that for every non-solvable subgroup G of SL(2,), the group G2 does not embed into Diff+1(S1).

Article information

Geom. Topol., Volume 14, Number 1 (2010), 573-584.

Received: 25 February 2009
Revised: 22 October 2009
Accepted: 19 October 2009
First available in Project Euclid: 20 December 2017

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Zentralblatt MATH identifier

Primary: 20B27: Infinite automorphism groups [See also 12F10] 37C85: Dynamics of group actions other than Z and R, and foliations [See mainly 22Fxx, and also 57R30, 57Sxx] 37E05: Maps of the interval (piecewise continuous, continuous, smooth)

Thurston's stability locally indicable group


Navas, Andrés. A finitely generated, locally indicable group with no faithful action by $C^1$ diffeomorphisms of the interval. Geom. Topol. 14 (2010), no. 1, 573--584. doi:10.2140/gt.2010.14.573.

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