We study a spectral sequence that computes the –equivariant homology of the free loop space of a manifold (the string homology of ). Using it and knowledge of the BV operations on , we compute the (mod 2) string homology of when is a sphere or a projective space.
"String homology of spheres and projective spaces." Algebr. Geom. Topol. 7 (1) 309 - 325, 2007. https://doi.org/10.2140/agt.2007.7.309