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Aequationes mathematicae

, Volume 79, Issue 1–2, pp 23–37 | Cite as

Reversible maps and composites of involutions in groups of piecewise linear homeomorphisms of the real line

  • Nick Gill
  • Ian Short
Article

Abstract

An element of a group is reversible if it is conjugate to its own inverse, and it is strongly reversible if it is conjugate to its inverse by an involution. A group element is strongly reversible if and only if it can be expressed as a composite of two involutions. In this paper the reversible maps, the strongly reversible maps, and those maps that can be expressed as a composite of involutions are determined in certain groups of piecewise linear homeomorphisms of the real line.

Mathematics Subject Classification (2000)

Primary 37E05 57S05 Secondary 57S25 

Keywords

Reversible involution piecewise linear 

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Copyright information

© Birkhäuser / Springer Basel AG 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity WalkBristolUK
  2. 2.Department of Pure Mathematics and Mathematical StatisticsCentre for Mathematical SciencesCambridgeUK

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