Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ON THE GAUSS MAP COMING FROM A FRAMING OF THE TANGENT BUNDLE OF A COMPACT MANIFOLD

  • Received : 2012.04.15
  • Published : 2013.01.31
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Abstract

Let W be a parallelizable compact oriented manifold of dimension $n$ with boundary ${\partial}W=M$. We define the so-called Gauss map $f:M{\rightarrow}S^{n-1}$ using a framing of TW and show that the degree of $f$ is equal to Euler-Poincar$\acute{e}$ number ${\chi}(W)$, regardless of the specific framing. As a special case, we get a Hopf theorem.

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References

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