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Consider the fiber bundle $S^{2n+1}\to \mathbb{CP}^n$, which has fiber $S^1$. All nonzero degree cohomology classes of $\mathbb{CP}^n$ are killed byIgnore this pull-back since the cohomology of $S^{2n+1}$ is zero in those degreesanswer.
Consider the fiber bundle $S^{2n+1}\to \mathbb{CP}^n$, which has fiber $S^1$. All nonzero degree cohomology classes of $\mathbb{CP}^n$ are killed by this pull-back since the cohomology of $S^{2n+1}$ is zero in those degrees.
Consider the fiber bundle $S^{2n+1}\to \mathbb{CP}^n$, which has fiber $S^1$. All nonzero degree cohomology classes of $\mathbb{CP}^n$ are killed by this pull-back since the cohomology of $S^{2n+1}$ is zero in those degrees.
