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.
