Bulletin of the Faculty of Education, Wakayama University. Natural science 68 1
2018-01-31 発行

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

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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DOI
Language
eng
Start Page
7
End Page
13
Keywords Alternative
Definable C∞G manifolds
definable C∞G maps
approximation theorem
definable C∞G vector bundles
definable C∞ fiber bundles
o-minimal
Abstract Alternative
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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