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

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 نشر من قبل Shizuo Kaji
 تاريخ النشر 2021
  مجال البحث
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 تأليف Shizuo Kaji




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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.



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