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**Harvard**

O'Farrell, A. och Roginskaya, M. (2009) *Reducing conjugacy in the full diffeomorphism group of ℝ to conjugacy in the subgroup of orientation-preserving maps*.

** BibTeX **

@article{

O'Farrell2009,

author={O'Farrell, A.G. and Roginskaya, Maria},

title={Reducing conjugacy in the full diffeomorphism group of ℝ to conjugacy in the subgroup of orientation-preserving maps},

journal={Journal of Mathematical Sciences},

issn={1072-3374},

volume={158},

issue={6},

pages={895-898},

abstract={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.},

year={2009},

}

** RefWorks **

RT Journal Article

SR Electronic

ID 237275

A1 O'Farrell, A.G.

A1 Roginskaya, Maria

T1 Reducing conjugacy in the full diffeomorphism group of ℝ to conjugacy in the subgroup of orientation-preserving maps

YR 2009

JF Journal of Mathematical Sciences

SN 1072-3374

VO 158

IS 6

SP 895

OP 898

AB 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.

LA eng

DO 10.1007/s10958-009-9419-x

LK http://dx.doi.org/10.1007/s10958-009-9419-x

OL 30