Topology Seminar: Gorenstein dimension and proper actions

Gedrich and Gruenberg(1987)and Ikenaga(1984) studied the algebraic invariants silp ZG,the supremum of the injective lengths of the projective ZG-modules,and spli,the supremum of the projective lengths of the injective ZG-modules,in connection with the existence of complete cohomological functors for the group G and showed that these are related to the virtual cohomological dimension of G. We will show that silpZG and spliZG are related to the Gorenstein dimension of ZG and to the existence of a finite dimensional model for E_G, the classifying space for proper actions.