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Göteborgs universitets publikationer

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

Författare och institution:
A.G. O'Farrell (-); Maria Roginskaya (Institutionen för matematiska vetenskaper, matematik, Chalmers/GU)
Publicerad i:
Journal of Mathematical Sciences, 158 ( 6 ) s. 895-898
ISSN:
1072-3374
E-ISSN:
1573-8795
Publikationstyp:
Artikel, refereegranskad vetenskaplig
Publiceringsår:
2009
Språk:
engelska
Fulltextlänk:
Sammanfattning (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.
Ämne (baseras på Högskoleverkets indelning av forskningsämnen):
NATURVETENSKAP ->
Matematik
Postens nummer:
237275
Posten skapad:
2016-06-03 12:10

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