DEFINABLE Cr FIBER BUNDLES AND DEFINABLE CrG VECTOR BUNDLES

Title & Authors
DEFINABLE Cr FIBER BUNDLES AND DEFINABLE CrG VECTOR BUNDLES
Kawakami, Tomohiro;

Abstract
Let G and K be compact subgroups of orthogonal groups and $\small{0{\leq}r}$<$\small{x}$<$\small{{\infty}}$. We prove that every topological fiber bundle over a definable $\small{C^r}$ manifold whose structure group is K admits a unique strongly definable $\small{C^r}$ fiber bundle structure up to definable $\small{C^r}$ fiber bundle isomorphism. We prove that every G vector bundle over an affine definable $\small{C^rG}$ manifold admits a unique strongly definable $\small{C^rG}$ vector bundle structure up to definable $\small{C^rG}$ vector bundle isomorphism.큺?⨀끹?⨀恸?⨀죽잖⨀处돀ᢰ?⨀⁊렼悚?⨀㄄돐肚?⨀ꢍ?⨀¸鉀㈰〱냫뎸곬鞅ကꇬ납鰀ऀἈ孍ⵚ䬿扜᠘䥇䰕阽뒳浇¸鉀0ꍀ଀ȀЀĀ¸鉀Ἀ孍ⵚ䬿¸鉀扜᠘䥇ᢘ?⨀ကĀ䰕阽뒳浇㢘?⨀ऀȀ扜᠘䥇墘?⨀က䰕阽뒳浇碘?⨀ऀl햨颗?⨀Ȁ扜᠘䥇𵾖⨀ကĀ䰕阽뒳浇?⨀ऀȀ㈰〱냫뎸곬鞅ꇬ납鰀㈰〱냫뎸곬鞅ꇬ납鰀㈰〱냫뎸곬鞅ꇬ납鰀¸鉀㈰〱냫뎸곬鞅ကꇬ납鰀ऀἈ孍ⵚ䬿扜᠘䥇䰕阽뒳浇¸鉀0ꍀ଀Ȁ؀Ā¸鉀Ἀ孍ⵚ䬿¸鉀扜᠘䥇ᢘ?⨀ကĀ䰕阽뒳浇㢘?⨀ऀȀ扜᠘䥇墘?⨀က䰕阽뒳浇碘?⨀ऀ飜?⨀颗?⨀ȀĀ?⨀Ȁ
Keywords
O-minimal;definable groups;definable $\small{C^r}$ groups;definable fiber bundles;definablp $\small{C^r}$ fiber bundles; definable G vector bundles;definable $\small{C^rG}$ vector bundles;
Language
English
Cited by
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