Algebraic & Geometric Topology

Nonsmoothable, locally indicable group actions on the interval

Danny Calegari

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By the Thurston Stability Theorem, a group of C1 orientation-preserving diffeomorphisms of the closed unit interval is locally indicable. We show that the local order structure of orbits gives a stronger criterion for nonsmoothability that can be used to produce new examples of locally indicable groups of homeomorphisms of the interval that are not conjugate to groups of C1 diffeomorphisms.

Article information

Algebr. Geom. Topol., Volume 8, Number 1 (2008), 609-613.

Received: 3 December 2007
Revised: 1 March 2008
Accepted: 1 March 2008
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

group action smoothable interval Thurston stability theorem order structure


Calegari, Danny. Nonsmoothable, locally indicable group actions on the interval. Algebr. Geom. Topol. 8 (2008), no. 1, 609--613. doi:10.2140/agt.2008.8.609.

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