If we have a smooth manifold $M$, why is the tangent bundle $TM$ trivial (as a vector bundle) iff the cotangent bundle $T^*M$ is trivial as well?
2026-04-06 10:56:34.1775472994
Trivial Tangent and Cotangent Bundles
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Hint: Given a global frame for either, there is a pretty natural way to create a global frame for the other by dualizing or taking the "covector".