Abstract

One of the important (but somehow isolated) results in rational equivariant homotopy theory is the splitting theorem of Greenlees-May/ Thévenaz-Webb for rational G-Mackey functors, where G is a finite group. This theorem, together with the description of the split pieces, has interesting consequences. In particular it implies that the category of rational G-Mackey functors is of homological dimension 0, when G is a finite group. In this talk I will present joint work with Dave Barnes and Mike Hill generalising the splitting to rational incomplete G-Mackey functors for finite G. Here incomplete refers to the existence of some, but perhaps not all, additive transfers. Such a situation is modelled by an $N_\infty$ – operad of Blumberg-Hill. I will also describe the split pieces and discuss some of the consequences of this result for the homological dimension of the category of rational incomplete G-Mackey functors.