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Nonsmoothable, locally indicable group actions on the interval

Danny Calegari

Algebraic & Geometric Topology 8 (2008) 609–613

DOI: 10.2140/agt.2008.8.609
Abstract

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.

Keywords

group action, smoothable, interval, Thurston stability theorem, order structure
Mathematical Subject Classification

Primary: 37C85

Secondary: 37E05
References
Publication

Received: 3 December 2007
Revised: 1 March 2008
Accepted: 1 March 2008
Published: 22 May 2008
Authors
Danny Calegari
Department of Mathematics
California Institute of Technology
Pasadena CA 91125
USA
http://www.its.caltech.edu/~dannyc