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If an $n-q$ dimensional cohomology class could cupped with that class, giving a class in $H^n$, and if that space comes equipped with a norm, you're in business.
For anyone learning the theory, I highly recommend looking at these notes: ma.utexas.edu/users/rhughes/TopicsInD-modules.pdf They are examples driven notes. Too bad more mathematics isn't taught this way!
