A zoo of diffeomorphism groups on $$\mathbb{R }^{n}$$Rn

@article{Michor2012AZO,
  title={A zoo of diffeomorphism groups on \$\$\mathbb\{R \}^\{n\}\$\$Rn},
  author={Peter W. Michor and David Mumford},
  journal={Annals of Global Analysis and Geometry},
  year={2012},
  volume={44},
  pages={529-540}
}
  • P. Michor, D. Mumford
  • Published 24 November 2012
  • Mathematics
  • Annals of Global Analysis and Geometry
We consider the groups $${\mathrm{Diff }}_\mathcal{B }(\mathbb{R }^n)$$DiffB(Rn), $${\mathrm{Diff }}_{H^\infty }(\mathbb{R }^n)$$DiffH∞(Rn), and $${\mathrm{Diff }}_{\mathcal{S }}(\mathbb{R }^n)$$DiffS(Rn) of smooth diffeomorphisms on $$\mathbb{R }^n$$Rn which differ from the identity by a function which is in either $$\mathcal{B }$$B (bounded in all derivatives), $$H^\infty = \bigcap _{k\ge 0}H^k$$H∞=⋂k≥0Hk, or $$\mathcal{S }$$S (rapidly decreasing). We show that all these groups are smooth… 
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