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