# cohomology with compact support

Where is the cohomology with compact support useful? It seems that, a part from proving Poincaré duality, we also use it to compute the top dimensional cohomology group of closed manifolds: isn't singular cohomology sufficient here?

Thanks

• Sufficient for what? – Mariano Suárez-Álvarez May 15 '11 at 14:49
• In any case it is easy to underestimate the importance and usefulness of having a cohomology theory with a nice duality property such as Poincaré duality. – Mariano Suárez-Álvarez May 15 '11 at 14:52
• @Mariano I meant sufficient to compute top dimensional cohomology group or module of a closed manifold – El Moro May 15 '11 at 15:02