Hi, this issue came up in another site:(adsbygoogle = window.adsbygoogle || []).push({});

We want to compute ( not just ) the deRham cohomology of ## X=\mathbb R^2 - ##{p,q} , but also

an explicit generating set for ## H^1 (X) = \mathbb Z (+) \mathbb Z## in deRham cohomology . Only explicit

generating set I can see here is {(0, +/- 1),(+/-1,0)}. How to map this into a pair of 1-forms that generate the first deRham cohomology?

We can get the actual cohomology using , e.g., Mayer Vietoris, but , without an explicit isomorphism, I don't see how to get a generating set. Maybe we can use the explicit maps in the

MV sequence to get some generators (in the deRham chain complex) ?

I was thinking of this: we compute ## H^1(X) ##, then we know all theories are equivalent, so this gives us singular cohomology , and then we use the explicit isomorphism in deRham's theorem to get some generators? We would see where the generators are sent.

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# Computing a Generating Set in Cohomology

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