Volume 8, issue 1 (2008)

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Nonsmoothable, locally indicable group actions on the interval

Danny Calegari

Algebraic & Geometric Topology 8 (2008) 609–613
Abstract

By the Thurston Stability Theorem, a group of ${C}^{1}$ 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 ${C}^{1}$ diffeomorphisms.

Keywords
group action, smoothable, interval, Thurston stability theorem, order structure
Primary: 37C85
Secondary: 37E05