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

Nick Gill·Ian Short
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Abstract

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.

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Nick Gill, Ian Short. 2008-02-01. Reversible maps and composites of involutions in groups of piecewise linear homeomorphisms of the real line. https://arxiv.org/abs/math/0702495

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