Real Algebraic and Analytic Geometry
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254. Tomohiro Kawakami:
Relative properties of definable C^\infty manifolds with finite abelian group actions in an o-minimal expansion of R_\exp.

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Submission: 2008, May 9.

Abstract:
We prove that every definable $C^{\infty} G$ manifold is affine. Moreover we prove that if $X_1, \dots, X_n$ (resp. $Y_1, \dots, Y_n$) are definable $C^{\infty} G$ submanifolds of a definable $C^{\infty} G$ manifold $X$ (resp. $Y$) in general position, then every definable $C^1 G$ map $(X; X_1, \dots, X_n) \to (Y; Y_1, \dots, Y_n)$ is approximated by a definable $C^{\infty} G$ map $(X; X_1, \dots, X_n) \to (Y; Y_1, \dots, Y_n)$ .

Mathematics Subject Classification (2000): 14P10, 14P20, 57S17, 58A05, 03C64.

Keywords and Phrases: O-minimal, definable C^{\infty} G manifolds, affineness, simultaneous definable C^{\infty} G approximations, relative collaring theorem.

Full text, 7p.: dvi 48k, ps.gz 110k, pdf 131k.