Fibration over a simply connected manifold

Question

Let $M$ and $N$ be smooth manifolds with $N$. Is a locally trivial fibration $f:M\to N$ is globally trivial if $N$ is simply connected?

You need $N$ to be contractible if you want your fibration to be trivial. — Nicolas Hemelsoet, Dec 30 '17 at 14:36
Could you give me a reference for the proof of this? Thanks. — Dino, May 16 '18 at 13:40

score 6 · Accepted Answer · answered Dec 30 '17 at 14:23

6

No, consider for example the Hopf fibration. https://en.wikipedia.org/wiki/Hopf_fibration

answered Dec 30 '17 at 14:23

Tsemo Aristide

1 Answers1