Regarding the parallelizability of the Milnor's seven dimensional exotic spheres: http://mathoverflow.net/questions/58131/parallelizability-of-the-milnors-exotic-spheres-in-dimension-7 The following question naturally arises: Suppose that a manifold has some exotic structures,and is parallelizable with respect to one of them ,is that manifold also parallelizable with respect to other smooth structures?
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