Finiteness obstructions of equivariant fibrations (Q1190724)

Let \(G\) be a compact Lie group. Generalizing the theory of \textit{C. T. C. Wall} [Ann. Math., II. Ser. 81, 56-69 (1965; Zbl 0152.219)], \textit{W. Lück} [Transformation groups and algebraic \(K\)-theory (Lect. Notes Math. 1408) (1989; Zbl 0679.57022)] defined an equivariant finiteness obstruction for a finitely dominated \(G\)-\(CW\)-complex which lies in a geometrically defined group and an equivariant Euler characteristic. Associated with a \(G\)-fibration \(F\to E\to B\), one obtains a transfer for these invariants, which is studied in the paper under discussion. Some vanishing results for the finiteness obstruction for the total space of a fibration are obtained in terms of the equivariant Euler characteristic of the fibre.