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Preprint Number 213
213. Tomohiro Kawakami Definable $C^{\infty} G$ manifold structures of definable $C^r G$
manifolds E-mail: Submission date: 10 November 2009. Abstract: Let G be a compact definable C^{\infty} group and 2 \le r < \infty. Let X be a noncompact affine definable C^r G manifold and X_1, \dots, X_k noncompact codimension one definable C^r G submanifolds of X such that X_1, \dots, X_k are in general position in X and (X;X_1, \dots, X_k) satisfies the frontier condition. We prove that (X;X_1, \dots, X_k) admits a unique definable C^{\infty} G manifold structure (Y; Y_1, \dots, Y_k). Mathematics Subject Classification: 14P10, 14P20, 58A05, 58A07, 03C64. Keywords and phrases: O-minimal, definable $C^{\infty} G$ manifolds, definable $C^r G$ manifolds, definable $C^{\infty} G$ compactifications, raising differentiability. |

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