Mod 2 cohomology of 2-compact groups of low rank

A bstract . We determine the mod 2 cohomology over the Steenrod algebra A 2 of the classifying spaces of the free loop groups LG for compact groups G = Spin (7), Spin (8), Spin (9), and F 4 . Then, we show that they are isomorphic as algebras over A 2 to the mod 2 cohomology of the corresponding Chevalley groups of type G ( q ), where q is an odd prime power. In a similar manner, we compute the cohomology of the free loop space over BDI (4) and show that it is isomorphic to that of BSol ( q ) as algebras over A 2 . This note is a revised version of [8].