Submission date: 18 July 2017

Abstract:

Let G and K be definably compact subgroups of orthogonal groups and 0 ≤ r < ∞. We prove that every definable fiber bundle over an affine 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.

Mathematics Subject Classification: MSC 2010 14P10, 14P20, 57S10, 57S15, 58A05, 58A07, 03C64.

Keywords and phrases: O-minimal, definable groups, definable C^r groups, definable fiber bundles, definable C^r fiber bundles, definable G vector bundles, definable C^r G vector bundles.

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