Vector Fields on the Sphere
In Chap. 12, Theorem (8.2), we saw that S n −1 has ρ(n) − 1 orthonormal tangent vector fields defined on it. The object of this chapter is to outline the steps required to prove that S n −1 does not have ρ(n) orthonormal tangent vector fields defined on it; in fact, S n −1 does not have ρ(n) linearly independent tangent vector fields; see also Adams .
KeywordsVector Bundle Line Bundle Spectral Sequence Group Morphism Cohomology Theory
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