Let $M,N$ be smooth manifolds and $C^\infty(M,N)$ be the function space with Whitney topology. 


If we know the cohomology groups of $M,N$, can we calculate the cohomology groups of $C^\infty(M,N)$?



Cohomology of function spaces
It seems there exists such a thing: There is a spectral sequence by Anderson that computes the homology of the mapping space out of the cohomology of $M$ and the homology of $N$. Here is a link to the announcement:


<http://www.ams.org/journals/bull/1972-78-05/S0002-9904-1972-13034-9/S0002-9904-1972-13034-9.pdf>


I have not been able to find the subsequent paper with the proof.


