\title{Mackey functors and sharpness for fusion systems}

\author{Antonio D\'iaz}



\address{Departamento de \'Algebra, Geometr\'ia y Topolog\'ia, 

		      Universidad de M\'alaga, 

		      Apdo correos 59, 

		      29080 M\'alaga, 

		      Spain}

\author{Sejong Park}



\address{School of Mathematics, Statistics and Applied Mathematics, 

		National University of Ireland, Galway, 

		University Road, Galway,

		Ireland}

\thanks{\rm The first author is supported by MICINN grant RYC-2010-05663 and partially supported by FEDER-MCI grant MTM2010-18089 and Junta de Andaluc{\'\i}a grant FQM-213.}





\begin{abstract}

We develop the fundamentals of Mackey functors in the setup of fusion systems including an acyclicity condition as well as a parametrization and an explicit description of simple Mackey functors. Using this machinery we extend Dwyer's sharpness results  to exotic fusion systems $\CF$ on a finite $p$-group $S$ with an abelian subgroup of index $p$.

\end{abstract}



To appear in Homology, Homotopy and Applications