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

Abstract

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).

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

Information

Received: 25 February 2009; Revised: 22 October 2009; Accepted: 19 October 2009; Published: 2010
First available in Project Euclid: 20 December 2017

zbMATH: 1197.37022
MathSciNet: MR2602845
Digital Object Identifier: 10.2140/gt.2010.14.573

Subjects:
Primary: 20B27 , 37C85 , 37E05

Keywords: locally indicable group , Thurston's stability

Rights: Copyright © 2010 Mathematical Sciences Publishers

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