String cohomology groups of complex projective spaces

Iver Ottosen, Marcel Bökstedt
2007 Algebraic and Geometric Topology  
Let 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. MSC: 55N91; 58E05; 55P35; 18G50
doi:10.2140/agt.2007.7.2165 fatcat:ro2vebc7ubf2lfosab3qnep4la