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Dec 11, 2009 at 5:02 comment added HJRW Another way of seeing this is to look at $\pi_2$. A non-trivial free product has an essential 2-sphere, whereas it's easy to see that the universal cover of a torus bundle is homeomorphic to $\mathbb{R}^3$.
Dec 11, 2009 at 2:16 history edited janmarqz CC BY-SA 2.5
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Dec 11, 2009 at 2:07 history answered janmarqz CC BY-SA 2.5