An affine definable CrG manifold admits a unique affine definable C∞G manifold structure

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  • アフィンデファイナブルCrG 多様体のアフィンデファイナブルC∞多様体構造について

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Let G be a compact subgroup of GLn(R). We prove that every affine definable CrG manifold admits a unique affine definable C∞G manifold structure up to definable C∞G diffeomorphism (1 ≦ r < ∞). Moreover we prove that every strongly definable CrG vector bundle over X admits a unique strongly definable C∞G vector bundle structure up to definable C∞G vector bundle isomorphism (0 ≦ r < ∞). Furthermore we consider raising differentiability of strong definable Cr fiber bundles (0 ≦ r < ∞).

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