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Michor","submitted_at":"2012-02-16T19:36:50Z","abstract_excerpt":"Given a finite dimensional manifold $N$, the group $\\operatorname{Diff}_{\\mathcal S}(N)$ of diffeomorphism of $N$ which fall suitably rapidly to the identity, acts on the manifold $B(M,N)$ of submanifolds on $N$ of diffeomorphism type $M$ where $M$ is a compact manifold with $\\dim M<\\dim N$. 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