Poincaré Conjecture/Dimension 4

Theorem
Let $\Sigma^4$ be a smooth $4$-manifold.

Let $\Sigma^4$ satisfy:
 * $H_0 \struct {\Sigma; \Z} = 0$

and:
 * $H_4 \struct {\Sigma; \Z} = \Z$

Then $\Sigma^4$ is homeomorphic to the $4$-sphere $\Bbb S^4$.

Proof
Follows from $4$-dimensional Topological $h$-Cobordism Theorem.