Abstract
The main result proved here is that B P ā ( E G Ć G X ) {\text {B}}{{\text {P}}_* }(EG{ \times _G}X) has finite homological dimension when G = Z p G = {{\mathbf {Z}}_p} and X X is a finite G - CW G{\text { - CW}} -complex. The argument uses B P ā BP {\text {B}}{{\text {P}}_*}{\text {BP}} -comodules.
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