Finite homological dimension of 𝐵𝑃_{∗}(𝑋) for infinite complexes

Abstract

The main result proved here is that B P ∗ ( E G × 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 ∗ BP {\text {B}}{{\text {P}}_*}{\text {BP}} -comodules.