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Abstract

It is known ([1], [2]) that a construction of equivariant finiteness obstructions leads to a family $w_α^H(X)$ of elements of the groups $K_0(ℤ [π_0(WH(X))_α^*])$. We prove that every family ${w_α^H}$ of elements of the groups $K_0(ℤ [π_0(WH(X))_α^*])$ can be realized as the family of equivariant finiteness obstructions $w^H_α(X)$ of an appropriate finitely dominated G-complex X. As an application of this result we show the natural equivalence of the geometric construction of equivariant finiteness obstruction ([5], [6]) and equivariant generalization of Wall's obstruction ([1], [2]).