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.

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - I. V. Usimov
TI  - Algebras of the equivariant cohomologies of an $\mathfrak F$-classifying $T^k$-spaces
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2015
SP  - 60
EP  - 70
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2015_1_a4/
LA  - ru
ID  - IVM_2015_1_a4
ER  - 
%0 Journal Article
%A I. V. Usimov
%T Algebras of the equivariant cohomologies of an $\mathfrak F$-classifying $T^k$-spaces
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2015
%P 60-70
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2015_1_a4/
%G ru
%F IVM_2015_1_a4
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/

[1] Ageev S. M., Repovsh D., “Zadacha o rasprostranenii nakryvayuschei gomotopii dlya kompaktnykh grupp preobrazovanii”, Matem zametki, 92:6 (2012), 803–818 | DOI | MR | Zbl

[2] Palais R., The classification of $G$-spaces, Mem. Amer. Math. Soc., 36, 1960 | MR | Zbl

[3] Ageev S. M., “Universalnye $G$-prostranstva Pale i izovariantnye absolyutnye ekstenzory”, Matem. sb., 203:6 (2012), 3–34 | DOI | MR | Zbl

[4] Ageev S. M., “Izovariantnye ekstenzory i kharakterizatsiya ekvivariantnykh gomotopicheskikh ekvivalentnostei”, Izv. RAN. Ser. matem., 76:5 (2012), 3–28 | DOI | MR | Zbl

[5] Syan U. I., Kogomologicheskaya teoriya topologicheskikh grupp preobrazovanii, Mir, M., 1979 | MR

[6] Ageev S. M., Usimov I. V., “The cohomology ring of subspace of universal $S^1$-space with finite orbit types”, Topology Appl., 160:11 (2013), 1255–1260 | DOI | MR | Zbl

[7] Bredon G. E., Equivariant cohomology theories, Lecture Notes in Math., 34, Springer-Verlag, Berlin–New York, 1967 | MR

[8] Fomenko A. T., Fuks D. V., Kurs gomotopicheskoi topologii, Nauka, M., 1989 | MR

[9] Morris S., Dvoistvennost Pontryagina i stroenie lokalno kompaktnykh abelevykh grupp, Mir, M., 1980 | MR | Zbl

[10] Bott R., Tu L. V., Differentsialnye formy v algebraicheskoi topologii, Nauka, M., 1989 | MR