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.

4 pages, 1 figure

Cited by in corpus (6)

• A finitely generated, locally indicable group with no faithful action by C^1 diffeomorphisms of the interval
• Free products and the algebraic structure of diffeomorphism groups
• Rigidity for $C^1$ actions on the interval arising from hyperbolicity I: solvable groups
• Hyperbolicity as an obstruction to smoothability for one-dimensional actions
• On free discrete subgroups of Diff(I)
• Direct products, overlapping actions, and critical regularity