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arXiv:math/0702495 [math.GR]AbstractReferencesReviewsResources

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

Nick Gill, Ian Short

Published 2007-02-16, updated 2008-02-01Version 4

An element of a group is \emph{reversible} if it is conjugate to its own inverse, and it is \emph{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.

Comments: 10 pages, 0 figures. Version 4 includes a few small clarifications and corrections. To appear in Aequationes Math
Categories: math.GR, math.DS
Subjects: 20E45, 37E05
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