Homology, Homotopy and Applications

Volume 17 (2015)

Number 1

Mackey functors and sharpness for fusion systems

Pages: 147 – 164

DOI: https://dx.doi.org/10.4310/HHA.2015.v17.n1.a7

Authors

Antonio Díaz (Departamento de Àlgebra, Geometría y Topología, Universidad de Málaga, Spain)

Sejong Park (School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland)

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 $\mathcal{F}$ on a finite $p$-group $S$ with an abelian subgroup of index $p$.

Keywords

homology decomposition, classifying space, higher limit, fusion system, Mackey functor

2010 Mathematics Subject Classification

20D20, 20J06, 55R35, 55R40

Published 18 May 2015