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Are the Milnor's seven dimensional exotic spheres parallelizable?

Inspried by this MO question A manifold whose tangent space is a sum of line bundles and higher rank vector bundles we pose the following question as a possible smooth version of the splitting ...

Let $M$ be a smooth manifold and let $A=C^\infty(M).$ We consider module of Kahler differentials $\Omega_k(A)$ and module of 1-forms $\Omega^1(M).$ Denote Kahler differential by $d_k$ and classical ...