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

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

2007-02-16

arxiv.org/abs/math/0702495v4

Mathematics

Group Theory

10 pages, 0 figures. Version 4 includes a few small clarifications and corrections. To appear in Aequationes Math

Scientific paper

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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