2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/112957Let X be a space and write LX for its free loop space equipped with the action of the circle group T given by dilation. We compute the equivariant cohomology H^*(LX_hT; Z/p) as a module over H^*(BT; Z/p) when X=CP^r for any positive integer r and any prime number p. The computation implies that the associated mod p Serre spectral sequence collapses from the E_3-page.61 pagesAlgebraic Topology55N91; 58E05; 55P35; 18G50text