On the Gauss map coming from a framing of the tangent bundle of a compact manifold
Commun. Korean Math. Soc. 2013 Vol. 28, No. 1, 183-189
https://doi.org/10.4134/CKMS.2013.28.1.183
Printed January 31, 2013
Yanghyun Byun and Daewoong Cheong
Hanyang University, Seoul National University
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\'{e} number $\chi{(W)}$, regardless of the specific framing. As a special case, we get a Hopf theorem.
Keywords : Gauss map, Hopf theorem
MSC numbers : 57R70, 58E05
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