\title{Bounded complexes of permutation modules}
\author{David J. Benson}
\author{Jon F. Carlson}
\thanks{The second author was partially supported by
Simons Foundation Grant 054813-01.}
\subjclass{20J06, 20C20}
\keywords{Finite groups, permutation modules, bounded exact complex}

\begin{document}

\begin{abstract}
Let $k$ be a field of characteristic $p > 0$. For $G$ an elementary abelian 
$p$-group, there exist collections of permutation module such that if $C^*$ 
is any exact bounded complex whose terms are sums of copies of modules from the 
collection, then $C^*$ is contractible. A consequence is that if $G$ is any
finite group whose Sylow $p$-subgroups are not cyclic or quaternion,
and if $C^*$ is a  bounded exact complex such that each $C^i$ is 
direct sum of one dimensional modules and projective modules, then $C^*$ 
is contractible. 
\end{abstract}