ON THE GAUSS MAP COMING FROM A FRAMING OF THE TANGENT BUNDLE OF A COMPACT MANIFOLD

Title & Authors
ON THE GAUSS MAP COMING FROM A FRAMING OF THE TANGENT BUNDLE OF A COMPACT MANIFOLD
Byun, Yanghyun; Cheong, Daewoong;

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