1
$\begingroup$

By the degree argument we see that any reflection on $\ S^{2n}$ is homotopic to the antipodal map.

But that seems a big theorem. I am looking for a straightforward argument.

  • 0
    I think you mean a reflection specifically in a hyperplane, right? For example, reflecting $S^2$ in any axis in $\mathbb{R}^3$ is a half-turn about that axis, which is homotopic to the identity map.2012-12-09

0 Answers 0