The Free Loop Space Homology of $(n-1)$-connected $2n$-manifolds

Our goal in this paper is to compute the integral free loop space homology of $(n-1)$-connected $2n$-manifolds $M$, $n\ge 2$. We do this when $n\mathrm{\ne }2,4,8$, or when $n\mathrm{\ne }2$ and ${\tilde{H}}^{\ast }(M)$ has trivial cup product squares, though the techniques used here should extend to a much wider range of manifolds. We also give partial information concerning the action of the Batalin-Vilkovisky operator.