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Reducing conjugacy in the full diffeomorphism group of ℝ to conjugacy in the subgroup of orientation-preserving maps

A.G. O'Farrell ; Maria Roginskaya (Institutionen för matematiska vetenskaper, matematik)
Journal of Mathematical Sciences (1072-3374). Vol. 158 (2009), 6, p. 895-898.
[Artikel, refereegranskad vetenskaplig]

Let Diffeo = Diffeo(ℝ) denote the group of infinitely differentiable diffeomorphisms of the real line ℝ, under the operation of composition, and let Diffeo+ be the subgroup of diffeomorphisms of degree +1, i.e., orientation-preserving diffeomorphisms. We show how to reduce the problem of determining whether or not two given elements f, g Diffeo are conjugate in Diffeo to associated conjugacy problems in the subgroup Diffeo+. The main result concerns the case when f and g have degree -1, and specifies (in an explicit and verifiable way) precisely what must be added to the assumption that their (compositional) squares are conjugate in Diffeo+, in order to ensure that f is conjugated to g by an element of Diffeo+. The methods involve formal power series and results of Kopell on centralisers in the diffeomorphism group of a half-open interval.

Denna post skapades 2016-06-03.
CPL Pubid: 237275


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