Given space $M=R^2/0$ ($R^2$ excluding origin), how to compute compactly supported de Rham cohomology of M, in notation, $H^*(c(M))$?
I am thinking of raising a vector v in $R^2$ with |v| at most some fixed length r, but this setup is not compact once you remove 0 from $R^2$. Therefore I wouldn't be using d operator on a compactly supported form (though I think d operator is necessary). So this just may not work...
Thanks for suggestions.