I have often heard quite a few times that they people talk about, say, "the" twisted S^2-bundle $S^2$-bundle over S^2. $S^2$. My question is, what do they mean by a twisted bundle? I know that in the above example any S^2-bundle $S^2$-bundle over S^2 $S^2$ is either S^2 x $S^2 or \times S^2$ or a unique non-trivial S^2-bundle $S^2$-bundle over S^2. but $S^2$. But is that how it is defined? I mean is Is a twisted bundle just a non-trivial one? , or is it a specific bundle among the non-trivial ones?
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twisted bundle definitionI have heard quite a few times that they talk about say, "the" twisted S^2-bundle over S^2. My question is what do they mean by a twisted bundle? I know that in the above example any S^2-bundle over S^2 is either S^2 x S^2 or or a unique non-trivial S^2-bundle over S^2. but is that how it is defined? I mean is a twisted bundle just a non-trivial one? or is it a specific bundle among the non-trivial ones?
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