Geodesic
The Covering Homotopy Extension Problem for Compact Transformation Groups
Matematičeskie zametki, Tome 92 (2012) no. 6, pp. 803-818.

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It is shown that the orbit space of universal (in the sense of Palais) $G$-spaces classifies $G$-spaces. Theorems on the extension of covering homotopy for $G$-spaces and on a homotopy representation of the isovariant category $\operatorname{ISOV}$ are proved.
Keywords: $G$-space, covering homotopy, universal $G$-space in the sense of Palais, absolute (neighborhood) extensor, classifying space.
Mots-clés : compact transformation group, orbit space 
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S. M. Ageev; D. D. Repovš. The Covering Homotopy Extension Problem for Compact Transformation Groups. Matematičeskie zametki, Tome 92 (2012) no. 6, pp. 803-818. http://geodesic.mathdoc.fr/item/MZM_2012_92_6_a0/

[1] R. S. Palais, The Classification of $G$-Spaces, Mem. Amer. Math. Soc., 36, Amer. Math. Soc., Providence, RI, 1960 | MR | Zbl

[2] S. M. Ageev, “Klassifikatsiya $G$-prostranstv”, Izv. RAN. Ser. matem., 56:6 (1992), 1345–1357 | MR | Zbl

[3] S. M. Ageev, “Izovariantnye ekstenzory”, Sib. matem. zhurn. (to appear)

[4] S. M. Ageev, “Ekstenzornye svoistva prostranstv orbit i zadacha prodolzheniya deistviya”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1994, no. 1, 11–16 | MR | Zbl

[5] S. M. Ageev, D. Repovsh, “O prodolzhenii deistvii grupp”, Matem. sb., 201:2 (2010), 3–28 | DOI | MR | Zbl

[6] T. tom Dieck, Transformation Groups, de Gruyter Stud. Math., 8, Walter de Gruyter, Berlin, 1987 | MR | Zbl

[7] T. tom Dik, Preobrazovaniya grupp i teoriya predstavlenii, Mir, M., 1982 | MR | Zbl

[8] S. Waner, “A generalization of the cohomology of groups”, Proc. Amer. Math. Soc., 85:3 (1982), 469–474 | DOI | MR | Zbl

[9] S. Waner, “Mackey functors and $G$-cohomology”, Proc. Amer. Math. Soc., 90:4, 641–648 | MR | Zbl

[10] J. P. May, Equivariant Homotopy and Cohomology Theory, CBMS Regional Conf. Ser. in Math., 91, Amer. Math. Soc., Providence, RI, 1996 | MR | Zbl

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

[12] G. E. Bredon, Vvedenie v teoriyu kompaktnykh grupp preobrazovanii, Nauka, M., 1980 | MR | Zbl

[13] K. Borsuk, Teoriya retraktov, Mir, M., 1971 | MR | Zbl

[14] L. S. Pontryagin, Nepreryvnye gruppy, Nauka, M., 1984 | MR | Zbl

[15] S. M. Ageev, “Ekvivariantnaya teorema Dugundzhi”, UMN, 45:5 (1990), 179–180 | MR | Zbl

[16] E. Spener, Algebraicheskaya topologiya, Mir, M., 1971 | MR | Zbl

[17] S.-T. Hu, Theory of Retracts, Wayne State University Press, Detroit, 1965 | MR | Zbl

[18] S. M. Ageev, “Klassifitsiruyuschie prostranstva dlya svobodnykh deistvii i gipoteza Gilberta–Smita”, Matem. sb., 183:1 (1992), 143–151 | MR | Zbl