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

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Abstract

We consider equivariant cohomologies generated by the Borel functor \(E_\mathfrak{F} \) for the family of orbit types \(\mathfrak{F}\) ⊂ Conj G , 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 \(\mathfrak{F}\) ⊂ Conj G in the case of actions of k-dimensional torus G = T k.

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  1. Belarus State University, pr. Nezavisimosti 4, Minsk, 200050, Republic of Belarus

    I. V. Usimov

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  1. I. V. Usimov
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Correspondence to I. V. Usimov.

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Original Russian Text © I.V. Usimov, 2015, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, No. 1, pp. 60–70.

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Usimov, I.V. Algebras of the equivariant cohomologies of an \(\mathfrak{F}\)-classifying T k-spaces. Russ Math. 59, 51–59 (2015). https://doi.org/10.3103/S1066369X15010053

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