On the gauss map coming from a framing of the tangent bundle of a compact manifold

초록

Let W be a parallelizable compact oriented manifold of di-mension n with boundary ∂W = M. We define the so-called Gauss map f: M →Sn-1 using a framing of TW and show that the degree of f is equal to Euler-Poincaré number χ(W), regardless of the specific framing. As a special case, we get a Hopf theorem.

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