Subject: isomorphisms of hopf bundles
From: villarini
Date: Fri, 29 Sep 2006 14:50:08 +0200
I would like to post the following question to people in the list (hoping
it is not toot trivial!..I am not a topologist..):
Question:
let S1-->S^2n+1-->CP^n be the hopf bundle
let S1-->S-->S/S1 be another circle bundle, and let S be diffeomorphic
(not equivariantly) to S^2n+1
Problem: is it true that the two bundles are always diffeomorphic, or
homeomorphic? (I think it is true if n=1 and probably false if n>1...)
In case of negative answer, can anyone suggest me a counterexample?
thank you, and best regards
massimo villarini
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