4
$\begingroup$

Suppose $f:S^2\rightarrow S^2$ is a diffeomorphism. Is true that $f$ must have a fixed point or a point $x\in S^2$ such that $f(f(x))=x$?

  • 0
    Yes. Have you learned the Lefschetz fixed point theorem yet?2012-12-12
  • 0
    No, give me some reference please @DavidSpeyer2012-12-12
  • 0
    Have you learned what cohomology is? If so, http://en.wikipedia.org/wiki/Lefschetz_fixed-point_theorem isn't bad.2012-12-12
  • 0
    Is there a more analytic way to solve this problem? Because i got it in a course of dynamical systems @DavidSpeyer2012-12-12
  • 0
    Not that I see. But I'm sure there are other approaches in the world. I'll leave it there.2012-12-12

0 Answers 0