Poincaré Conjecture/Dimension 3

Theorem
Let $\Sigma^3$ be a smooth $3$-manifold.

Let $\Sigma^3$ satisfy:
 * $H_0 \struct {\Sigma; \Z} = 0$

and:
 * $H_3 \struct {\Sigma; \Z} = \Z$

Then $\Sigma^3$ is homeomorphic to the $3$-sphere $\Bbb S^3$.

Proof
Follows from Thurston's Geometrization Conjecture.