• Title/Summary/Keyword: definablp $C^r$ fiber bundles

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DEFINABLE Cr FIBER BUNDLES AND DEFINABLE CrG VECTOR BUNDLES

  • Kawakami, Tomohiro
    • Communications of the Korean Mathematical Society
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    • v.23 no.2
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    • pp.257-268
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    • 2008
  • Let G and K be compact subgroups of orthogonal groups and $0{\leq}r<x<{\infty}$. We prove that every topological fiber bundle over a definable $C^r$ manifold whose structure group is K admits a unique strongly definable $C^r$ fiber bundle structure up to definable $C^r$ fiber bundle isomorphism. We prove that every G vector bundle over an affine definable $C^rG$ manifold admits a unique strongly definable $C^rG$ vector bundle structure up to definable $C^rG$ vector bundle isomorphism.