Let $f$ be a map from the real projective plane to the torus. Show that $f$ must be homotopic to a constant map.

Question

Let $f$ be a map from the real projective plane to the torus. Show that $f$ must be homotopic to a constant map. This is a qual problem. Any help would be appreciated. Thank you.

score 1 · Answer 1 · answered Feb 19 '13 at 18:26

1

Since the universal cover of the torus is contractible, it's enough to show that such a map must lift to the universal cover. When does that happen?

answered Feb 19 '13 at 18:26

Jason DeVito - on hiatus

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(I can provide more of a hint later on, if you'd like) – Jason DeVito - on hiatus Feb 19 '13 at 18:27

Let $f$ be a map from the real projective plane to the torus. Show that $f$ must be homotopic to a constant map.

1 Answers1