Group Actions on Algebraic Cell Complexes

Abstract

We establish an algebraic version of the classical result that a $G$-map $f$ between $G$-complexes which restricts to a homotopy equivalence $f^H$ on $H$-fixed sets for all subgroups $H$ of $G$ is a $G$-homotopy equivalence. This is used to give an alternative proof of a theorem of Bouc. We also include a number of illustrations and applications.