Algebras of the equivariant cohomologies of an $\mathfrak{F}$ -classifying T k -spaces

Abstract

We consider equivariant cohomologies generated by the Borel functor \(E_\mathfrak{F} \) for the family of orbit types \(\mathfrak{F}\) ⊂ ConjG, which translates equivariant homotopy category EQUIV-HOMOT in \(\mathfrak{F}\)-isovariant homotopy category \(ISOV_\mathfrak{F} \)-HOMOT. Due to the effect of concentration of isovariant absolute extensors \(ISOV_\mathfrak{F} \)-AE we calculate in explicit form the algebra of equivariant cohomologies of an \(\mathfrak{F}\)-classifying G-spaces for finite families of orbit types \(\mathfrak{F}\) ⊂ ConjG in the case of actions of k-dimensional torus G = Tk.