Category:Poincaré Conjecture

This category contains pages concerning Poincaré Conjecture:

Let $\Sigma^m$ be a smooth $m$-manifold.

Let $\Sigma^m$ satisfy:

$H_0 \struct {\Sigma; \Z} = 0$

and:

$H_m \struct {\Sigma; \Z} = \Z$

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