ID 3272
FullText File
Title Alternative
An affine definable CrG manifold admits a unique affine definable C∞G manifold structure
Authors
DOI
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
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