5
votes
2answers
233 views

The fundamental group of a $3$-manifold with a boundary of genus $>0$

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) ...
3
votes
3answers
258 views

When is a three-manifold deck transformation group solvable?

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 ...
14
votes
3answers
613 views

3-manifolds with solvable fundamental group

Is there a nice reference for the classification of closed 3-manifolds with solvable (nilpotent, abelian, etc.) fundamental group, assuming the Geometrization Conjecture?
3
votes
2answers
462 views

Fundamental groups of closed hyperbolic 3-manifolds are freely indecomposable

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. ...