Category:Poincaré Duality Theorem

This category contains pages concerning Poincaré Duality Theorem:

Let $M$ be an $n$-manifold.

Let its $n$th homology group $\map {H_n} M$ be infinite and cyclic (that is, that $M$ is an orientable manifold).

Then $\map {H_r} M$ is homeomorphic to the $\paren {n - r}$th cohomology group $\map {H^{n - r} } M$ for all $r$.

Source of Name

This entry was named for Jules Henri Poincaré.