On the classifying space and cohomology of Thompson's sporadic simple group

D. J. Benson

To John Thompson on the occasion of his 70th birthday.

\begin{abstract}
This paper examines the classifying space
of Thompson's sporadic simple group. Two theorems are proved.
The first gives a homotopy colimit decomposition for
the $2$-completion of the classifying space. The second shows
that the mod two cohomology contains a copy of the Dickson
invariants of rank five, over which it is finitely generated
as a module.
\end{abstract}