A new approach to mod 2 decompositions of BSU(2) and BSO(3)

Loop space homology associated to the mod 2 Dickson invariants

The spaces BG_2 and BDI(4) have the property that their mod 2 cohomology is given by the rank 3 and 4 Dickson invariants respectively. Associated with these spaces one has for q odd the classifying spaces of the finite groups BG_2(q)and the exotic family of classifying spaces of 2-local finite groups BSol(q). In this article compute the mod 2 loop space homology of the 2-completed classifying space of G_2(q) and of BSol(q) for all odd primes q, as algebras over the Steenrod algebra, and the associated Bockstein spectral sequences.

A₄和SO(3)的模2上同调中Steenrod闭参数理想

Steenrod closed parameter ideals in the mod-$2$ cohomology of $A_4$ and $SO(3)$

本文分类了A₄和SO(3)模2上同调中Steenrod闭参数理想，进而得到这两个群可自由作用于Sⁿ×Sᵐ时维度n,m的限制。

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

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.