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Michor","submitted_at":"2012-11-24T20:37:18Z","abstract_excerpt":"We consider the groups $\\operatorname{Diff}_{\\mathcal B}(\\mathbb R^n)$, $\\operatorname{Diff}_{H^\\infty}(\\mathbb R^n)$, and $\\operatorname{Diff}_{\\mathcal S}(\\mathbb R^n)$ of smooth diffeomorphisms on $\\mathbb R^n$ which differ from the identity by a function which is in either $\\mathcal B$ (bounded in all derivatives), $H^\\infty = \\bigcap_{k\\ge 0}H^k$, or $\\mathcal S$ (rapidly decreasing). 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