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

Gill, Nick and Short, Ian (2010). Reversible maps and composites of involutions in groups of piecewise linear homeomorphisms of the real line. Aequationes Mathematicae, 79(1-2) pp. 23–37.

DOI: https://doi.org/10.1007/s00010-010-0002-9

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.

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