Let $M$ be an orientable $3$-manifold with connected boundary $\Sigma_g$, a surface of genus $g>0$. I would like to find a reference to the following two statements. 1) $\pi_1(M)\ne 0$. 2) ...
Suppose that $\pi:Y \to Y'$ is a regular covering of closed, connected, orientable three-manifolds and let $G$ be the deck transformation group. Furthermore, suppose that $Y$ is a rational homology ...
Is there a nice reference for the classification of closed 3-manifolds with solvable (nilpotent, abelian, etc.) fundamental group, assuming the Geometrization Conjecture?
I believe the following statement is true, and I've even seen it referenced here. Could someone point me to a proof? The fundamental group of a closed hyperbolic 3-manifold is not a free product. ...