Nonsmoothable, locally indicable group actions on the interval

Calegari, Danny

doi:10.2140/agt.2008.8.609

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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 $C^{1}$ 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

Mathematical Subject Classification 2000

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

Volume 8, issue 1 (2008)