Mod 2 cohomology of 2-local finite groups of low rank

Abstract

We determine the mod $2$ cohomology over the Steenrod algebra 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 the Steenrod algebra 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 the Steenrod algebra.

arXiv commentThis is a revised version of "Mod 2 cohomology of 2-compact groups of low rank", J. of Math. of Kyoto Univ. 47 (2007), no. 2, 441--450

Cited by in corpus (1)

• Cohomology of classifying spaces of loop groups and finite Chevalley groups associated with spin groups