# 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

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Sufficient for what? –  Mariano Suárez-Alvarez 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-Alvarez 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