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

ID	3272
FullText File	AN00257977.68(1).7.pdf 152 KB
Title Alternative	An affine definable CrG manifold admits a unique affine definable C∞G manifold structure
Authors	KAWAKAMI, Tomohiro Faculty of Education 和歌山大学研究者総覧 researchmap
Self DOI	10.19002/AN00257977.68(1).7
Journal Title	Bulletin of the Faculty of Education, Wakayama University. Natural science
ISSN	13424645
NCID	AN00257977
Volume	68
Issue	1
Start Page	7
End Page	13
Order	02
Published Date	2018-01-31
Language	eng
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 < ∞).
Content Type	Departmental Bulletin Paper
Text Version	publisher