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YCor
YCor
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Let $M^3$ be a compact $3$-manifold such that $\pi_1(M)$ contains a normal subgroup isomorphic to $\mathbb Z$.

Can we show either $\pi_1(M)$ is torsion free-free or $\pi_1(M)=\mathbb Z \oplus \mathbb Z_2$ or $\mathbb Z_2 * \mathbb Z_2$?

Let $M^3$ be a compact $3$-manifold such that $\pi_1(M)$ contains a normal subgroup isomorphic to $\mathbb Z$.

Can we show either $\pi_1(M)$ is torsion free or $\pi_1(M)=\mathbb Z \oplus \mathbb Z_2$ or $\mathbb Z_2 * \mathbb Z_2$?

Let $M^3$ be a compact $3$-manifold such that $\pi_1(M)$ contains a normal subgroup isomorphic to $\mathbb Z$.

Can we show either $\pi_1(M)$ is torsion-free or $\pi_1(M)=\mathbb Z \oplus \mathbb Z_2$ or $\mathbb Z_2 * \mathbb Z_2$?

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Zhiqiang
Zhiqiang
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$\pi_1(M^3)$ containing a normal infinite cyclic subgroup

Let $M^3$ be a compact $3$-manifold such that $\pi_1(M)$ contains a normal subgroup isomorphic to $\mathbb Z$.

Can we show either $\pi_1(M)$ is torsion free or $\pi_1(M)=\mathbb Z \oplus \mathbb Z_2$ or $\mathbb Z_2 * \mathbb Z_2$?