For given $\infty \ge k_1 \ge k_2 \ge 0$, are there non-trivial $C^{k_1}$ vector bundles over a "sufficiently nice" space that are trivial as a $C^{k_2}$ fibre bundle? How nice can the space be and still admit counter-examples?
2026-03-26 18:57:10.1774551430
Non-trivial $C^{k_1}$ vector bundle that is trivial as $C^{k_2}$ fibre bundle
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