Nonsmoothable, locally indicable group actions on the interval

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.