String homology of spheres and projective spaces

Abstract

We study a spectral sequence that computes the $S^1$–equivariant homology of the free loop space $LM$ of a manifold $M$ (the string homology of $M$). Using it and knowledge of the BV operations on $H{H}^{\ast }\left(H^{\ast }\left(M\right),H^{\ast }\left(M\right)\right)$, we compute the (mod 2) string homology of $M$ when $M$ is a sphere or a projective space.