Geodesic
Algebras of the equivariant cohomologies of an $\mathfrak F$-classifying $T^k$-spaces
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2015), pp. 60-70

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We consider equivariant cohomologies generated by the Borel functor $ E_\mathfrak F$ for the family of orbit types $\mathfrak F\subset\mathrm{Conj}_G$, which translates equivariant homotopy category EQUIV-HOMOT in $\mathfrak F$-isovariant homotopy category $\mathrm{ISOV}_\mathfrak F$-$\mathrm{HOMOT}$. Due to the effect of concentration of isovariant absolute extensors $\mathrm{ISOV}_\mathfrak F$-$\mathrm{AE}$ we calculate in explicit form the algebra of equivariant cohomologies of an $\mathfrak F$-classifying $G$-spaces for finite families of orbit types $\mathfrak F\subset\mathrm{Conj}_G$ in the case of actions of $k$-dimensional torus $G=T^k$.
Mots-clés : equivariant cohomologies, universal Palais $G$-space.
Keywords: classifying $G$-spaces, isovariant absolute extensor 
@article{IVM_2015_1_a4,
     author = {I. V. Usimov},
     title = {Algebras of the equivariant cohomologies of an $\mathfrak F$-classifying $T^k$-spaces},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {60--70},
     publisher = {mathdoc},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2015_1_a4/}
}
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I. V. Usimov. Algebras of the equivariant cohomologies of an $\mathfrak F$-classifying $T^k$-spaces. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2015), pp. 60-70. http://geodesic.mathdoc.fr/item/IVM_2015_1_a4/