MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

It is well-known (see Kuiper's theorem) that every Hilbert space bundle over a manifold is trivial if the Hilbert space is truly infinite-dimensional.

Does the same hold true if one considers locally trivial fiber bundles instead and the fiber is assumed to be a truly infinite dimensional Hilbert manifold?

share|cite|improve this question
What do you mean by "truly" infinite dimensional Hilbert manifold? You can easily build a fiber bundle over $S^1$ with fiber $S^1 \times H$, $H$ a Hilbert space, which is non-trivial just by homotopy reasons. – Alberto Abbondandolo May 2 '12 at 13:08
Dear Alberto, your comments answers my question. Thanks! – Orbicular May 3 '12 at 7:34
You are welcome. Ciao! – Alberto Abbondandolo May 3 '12 at 20:26

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.