How to calculate the DeRham cohomology of the free loop space $LM= C^\infty(S^1,M)$ as a Frechet manifold?. 


Edit: It will be enough for me to know: 
When $H^1\_{DR}(LM)$ is not $\{0\}$. 


Bounty is ending within 5 hours. 



Loop space: De Rham cohomology
An equivariant de Rham theory in precisely this setting seems to be developed by Leandre in "Equivariant Cohomology, Fock Space and Loop Groups" (2006). (<http://www.mth.kcl.ac.uk/staff/fa_rogers/ECFSLG.pdf>)


