A zoo of diffeomorphism groups on ℝⁿ R n

2012/11/30 by Peter W. Michor, David Mumford · 2 citations
Mathematics · #Analytic and geometric function theory #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.DG #math.FA #msc:58B20 #msc:58D15

paper · pdf · doi:10.1007/s10455-013-9380-2

published as Annals of Global Analysis and Geometry 44, 4 (2013), 529-540 · 12 pages. Revised: Misprints and mistakes corrected

arxiv created 2013/05/06 · openalex publication_date 2013/05/23 · arxiv updated 2014/10/07 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We consider the groups Diff_{\mathcal B}(\mathbb Rⁿ), Diff_H^∞(\mathbb Rⁿ), and Diff_{\mathcal S}(\mathbb Rⁿ) of smooth diffeomorphisms on \mathbb Rⁿ which differ from the identity by a function which is in either \mathcal B (bounded in all derivatives), H^∞ = \bigcap_{k≥ 0}H^k, or \mathcal S (rapidly decreasing). We show that all these groups are smooth regular Lie groups.

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• Flat Bundles on Function Manifolds and Evolution Equations in Quantum Field Theories
• Diffeomorphism [wikipedia]

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