Let G be a compact Lie group and E?B a G-fibration. We define a homomorphism WaG(B)?UG(B) into WaG(E)?UG(E) sending the pair of the finiteness obstruction of B and the equivariant Euler characteristic of B to that of E. Here WaG is the functor from the G-homotopy category of finitely dominated G-CW complexes into the category of abelian groups given by W. Lück. By making use of this, we show that if H and K are closed subgroups with H or K normal such that W(HK) is not finite, G HX is K-homotopy equivalent to a finite K-CW complex.
|ジャーナル||Publications of the Research Institute for Mathematical Sciences|
|出版ステータス||出版済み - 1 1 1991|
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