Abstract
Let G and K be compact subgroups of orthogonal groups and <TEX>$0{\leq}r</TEX><TEX><</TEX><TEX>x</TEX><TEX><</TEX><TEX>{\infty}$</TEX>. We prove that every topological fiber bundle over a definable <TEX>$C^r$</TEX> manifold whose structure group is K admits a unique strongly definable <TEX>$C^r$</TEX> fiber bundle structure up to definable <TEX>$C^r$</TEX> fiber bundle isomorphism. We prove that every G vector bundle over an affine definable <TEX>$C^rG$</TEX> manifold admits a unique strongly definable <TEX>$C^rG$</TEX> vector bundle structure up to definable <TEX>$C^rG$</TEX> vector bundle isomorphism.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
