Relative properties of definable C∞ manifolds with finite abelian group actions in an o-minimal expansion of Rexp
نویسنده
چکیده
zw Let G be a finite abelian group and M an o-minimal expansion of Rexp = (R, +, ·, <, e) admitting the C∞ cell decomposition. Everything is considered in M. We prove that every definable C∞G manifold is affine. Moreover we prove that if X1, . . . , Xn (resp. Y1, . . . , Yn) are definable C ∞G submanifolds of a definable C∞G manifold X (resp. Y ) in general position, then every definable CG map (X; X1, . . . , Xn) → (Y ; Y1, . . . , Yn) is approximated by a definable C∞G map (X; X1, . . . , Xn) → (Y ; Y1, . . . , Yn). Furthermore we prove a relative collaring theorem. 2000 Mathematics Subject Classification. 14P10, 14P20, 57S17, 58A05, 03C64.
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