Dimension functions of homotopy representations for compact Lie groups (Q1821395)

An h-representation is a G-CW complex, such that the fixed point set of any subgroup is a sphere. The dimension function of an h-representation, restricted to a certain class of subgroups, can be related to a virtual representation. This linearity theorem reduced the problem ''Which functions can be realized as dimension functions ?'' to the finite group case. The proof uses the concept of niltoral groups. In particular a compact Lie group admits an h-representation with non-stably linear dimension function iff it is not niltoral. This generalizes results of tom Dieck on finite groups and tori.