Abstract
AbstractThe fact that no real Grassmann manifolds Gk(Rn) are parallelizable (or even stably parallelizable) except for the obvious cases G1R2≅S1, G1(R4)≅G3(R4) ≅ RP3, and G1(R8)≅ G7(R8) ≅ RP7 was first noted by Hiller and Stong. Their work in turn depends on induction and the work of Oproiu, who examined detailed calculations of Stiefel-Whitney classes for k = 2, 3. In this note we give a short proof of this result, using elementary results from K-theory, that also covers the complex and quaternionic Grassmann manifolds.
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