# Is there an analogue of the hopf fibration for the hemisphere off $S^3$?

The Hopf fibration represents the 3-sphere $S^3$ as the circle $S^1$ fibred over the 2-sphere $S^2$. Does a similar construction exist for the hemisphere of $S^3$?

## 1 Answer

The hemisphere is contractible so any fiber bundle over it would be trivial.

• I would say that as the hemisphere is contractible it cannot be a circle bundle.. – Thomas Jul 11 '17 at 16:40
• Ah ok, I thought he meant bundles over the hemisphere. – Horstenson Jul 11 '17 at 17:50