| Abstract: | A standing conjecture in  -cohomology says that every finite  -complex  is of  -determinant class. In this paper, we prove this whenever the fundamental group belongs to a large class  of groups containing, e.g., all extensions of residually finite groups with amenable quotients, all residually amenable groups, and free products of these. If, in addition,  is  -acyclic, we also show that the  -determinant is a homotopy invariant -- giving a short and easy proof independent of and encompassing all known cases. Under suitable conditions we give new approximation formulas for  -Betti numbers. |
