Volume 14, issue 1 (2010)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
A finitely generated, locally indicable group with no faithful action by $C^1$ diffeomorphisms of the interval

Andrés Navas

Geometry & Topology 14 (2010) 573–584
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 F2 2, 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 G 2 does not embed into Diff+1(S1).

Keywords
Thurston's stability, locally indicable group
Mathematical Subject Classification 2000
Primary: 20B27, 37C85, 37E05
References
Publication
Received: 25 February 2009
Revised: 22 October 2009
Accepted: 19 October 2009
Published: 26 January 2010
Proposed: Danny Calegari
Seconded: Leonid Polterovich and Yasha Eliashberg
Authors
Andrés Navas
Departamento de Matemáticas
Facultad de Ciencia
Universidad de Santiago de Chile
Alameda 3363
Santiago
Chile