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I know that a torus the product of circles. But what the fundamental group of the product of a 3-sphere and a circle? ie $\pi_1((S^3 \times S^1), (1,1))$?

Thanks!

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    The fundamental group of a product is the product of the fundamental groups. Since $\pi_1(S^3)=\{0\}$, that means that the fundamental group is just $\pi_1(S^1)=\mathbb Z$2011-11-30

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