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 $\mathbb Z_2 * \mathbb Z_2$?
$\pi_1(M^3)$ containing a normal infinite cyclic subgroup
Zhiqiang
- 891
- 3
- 11