Let be a space and write for its free loop space equipped with the action of the circle group given by dilation. The equivariant cohomology is a module over . We give a computation of this module when for any positive integer and any prime number . The computation does not use the fact that is formal, nor does it use the Jones isomorphism and negative cyclic homology.
"String cohomology groups of complex projective spaces." Algebr. Geom. Topol. 7 (4) 2165 - 2238, 2007. https://doi.org/10.2140/agt.2007.7.2165