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$\begingroup$Coefficients in $\mathbb Z$?$\endgroup$
– Fernando MuroJun 20 '13 at 17:36
$\begingroup$There is paper by Loday "Free loop space and homology". It establishes isomorphism between cohomology of free loop space $LX$ and Hochschild homology of an algebra of singular cochains $S^*X$. Maybe this will help.$\endgroup$
– Sasha PatotskiJun 20 '13 at 17:37
$\begingroup$@Fernando Muro, Yes. But \mathbb{Q} coefficeints is also fine. @Sasha Patotski, thanks, I will have a look.$\endgroup$
– Murat SaglamJun 21 '13 at 14:49
$\begingroup$Do you mean for each component of the free loop space? The free loop space $LM$ has $p$ components for the lens space $M=L(p,q)$.$\endgroup$
– Somnath BasuAug 30 '13 at 14:26