0
$\begingroup$

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 $S^3$?

$\endgroup$
1
$\begingroup$

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

$\endgroup$
  • 1
    $\begingroup$ I would say that as the hemisphere is contractible it cannot be a circle bundle.. $\endgroup$ – Thomas Jul 11 '17 at 16:40
  • $\begingroup$ Ah ok, I thought he meant bundles over the hemisphere. $\endgroup$ – Horstenson Jul 11 '17 at 17:50

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.