Geometry & Topology
- Geom. Topol.
- Volume 14, Number 1 (2010), 573-584.
A finitely generated, locally indicable group with no faithful action by $C^1$ diffeomorphisms of the interval
According to Thurston’s stability theorem, every group of 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 , although locally indicable, does not embed into . (Here is any free subgroup of , and its action on is the linear one.) Moreover, we show that for every non-solvable subgroup of , the group does not embed into .
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
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
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)
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. https://projecteuclid.org/euclid.gt/1513732182