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

川上, 智博

68 ( 1 )  , pp.7 - 13 , 2018-01-31
ISSN:13424645
NCID:AN00257977
Description
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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http://repository.center.wakayama-u.ac.jp/files/public/0/3272/20180820134543440173/AN00257977.68(1).7.pdf

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