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We are given an $R^4$ bundle $\xi$ over $S^4$, whose total space is E, and we know that the associated sphere bundle is the Hopf fibration $S^3 \rightarrow S^7 \rightarrow S^4$. How can we show that the total space E' of the associated disk bundle is $HP^2-$ an open 8-cell?

I know that the Thom space $T$ of $\xi$ is obtained from $E'$ by gluing a cone over $\partial E'\approx S^7$ and cell decomposition of $T$ is the same as that of $HP^2$. But I cannot combine these..

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