Borsuk-Ulam theorem and Stiefel manifolds
Borsuk-Ulam theorem and Stiefel manifolds
There are several different, but equivalent versions of the classical Borsuk- Ulam theorem.One of them can be stated as follows:THE CLASSICAL BORSUK-URM THEOREM.Let $S^{n}$ be the unit sphere in euclidean $(n+1)$ -space $R^{n+1}$ .If $f:S^{n}arrow R^{n}$ is a $Z_{2}$ -map, $i$ .$e.$ , satisfies $f(-x)=$ $-f(x)$ for all $x\in S^{n}$ …