Reversibility in the group of homeomorphisms of the circle

Gill, Nick; O'Farrell, Anthony G. and Short, Ian (2009). Reversibility in the group of homeomorphisms of the circle. Bulletin of the London Mathematical Society, 41(5) pp. 885–897.

DOI: https://doi.org/10.1112/blms/bdp065

Abstract

The group of orientation-preserving homeomorphisms of the circle is simple, and, because there are non-trivial involutions in this group, it must be generated by its involutions. We show that, in this group of homeomorphisms, each element can be expressed as a product of three involutions. We also characterise those elements of the group that can be expressed as a composite of two involutions, and perform a similar characterisation in the full group of homeomorphisms of the circle.

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