Geodesic
A characterization of the free actions of zero-dimensional compact groups on $k$-dimensional Menger compacta
Izvestiya. Mathematics, Tome 59 (1995) no. 2, pp. 229-270 
S. M. Ageev. A characterization of the free actions of zero-dimensional compact groups on $k$-dimensional Menger compacta. Izvestiya. Mathematics, Tome 59 (1995) no. 2, pp. 229-270. http://geodesic.mathdoc.fr/item/IM2_1995_59_2_a0/
@article{IM2_1995_59_2_a0,
     author = {S. M. Ageev},
     title = {A characterization of the free actions of zero-dimensional compact groups on $k$-dimensional {Menger} compacta},
     journal = {Izvestiya. Mathematics},
     pages = {229--270},
     year = {1995},
     volume = {59},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1995_59_2_a0/}
}
TY  - JOUR
AU  - S. M. Ageev
TI  - A characterization of the free actions of zero-dimensional compact groups on $k$-dimensional Menger compacta
JO  - Izvestiya. Mathematics
PY  - 1995
SP  - 229
EP  - 270
VL  - 59
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/IM2_1995_59_2_a0/
LA  - en
ID  - IM2_1995_59_2_a0
ER  - 
%0 Journal Article
%A S. M. Ageev
%T A characterization of the free actions of zero-dimensional compact groups on $k$-dimensional Menger compacta
%J Izvestiya. Mathematics
%D 1995
%P 229-270
%V 59
%N 2
%U http://geodesic.mathdoc.fr/item/IM2_1995_59_2_a0/
%G en
%F IM2_1995_59_2_a0

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

This paper contains a theorem characterizing free actions of a zerodimensional compact group $G$ on a $k$-dimensional Menger compactum $\mu^k$: two free actions $\alpha\colon G\times\mu^k\to\mu^k$ and $\alpha_1\colon G\times\mu^k\to\mu^k$ are equivalent provided that the dimensions of the orbit spaces are equal to $k$ and the actions are strongly universal with respect to the class of free compacta $Y$ with $\dim(Y/G)\leqslant k$. This theorem, as well as other results of the paper, suggest that, in the category of compact spaces equipped with free actions of groups of the above type, there are distinguished objects (referred to in what follows as free Menger compacta $\mu^k_f$), with properties analogous to those of the classical Menger compacta $\mu^k$.

[1] Dranishnikov A. N., “O svobodnykh deistviyakh nulmernykh kompaktnykh grupp”, Izv. AN SSSR. Ser. matem., 52:1 (1988), 212–228 | MR | Zbl

[2] Ageev S. M., “Klassifitsiruyuschie prostranstva dlya svobodnykh deistvii i gipoteza Gilberta–Smita”, Matem. sb., 183:1 (1992), 143–152 | MR

[3] Bredon G. E., Raymond F., Williams R. F., “$p$-Adic groups transformation”, Trans. AMS, 99 (1961), 488–498 | DOI | MR | Zbl

[4] Bestvina M., Characterizing $k$-dimensional universal Menger compacta, Diss. Dr. Ph. Degree, The Univ. of Tennessee, Knoxville, 1984 | MR

[5] Torunczyk H., “On $CE$-images of the Hilbert cube and characterization of $Q$-manifolds”, Fund. Math., 106 (1980), 31–40 | MR | Zbl

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

[7] Rurk K., Sanderson B., Vvedenie v kusochno lineinuyu topologiyu, Mir, M., 1974 | MR

[8] Pontryagin L. S., Nepreryvnye gruppy, Nauka, M., 1973 | MR | Zbl

[9] Aleksandrov P. S., Pasynkov B. A., Vvedenie v teoriyu razmernosti, Nauka, M., 1973 | MR

[10] Illman S., “The equivariant triangulation theorem for action of compact Lie groups”, Math. Ann., 262 (1983), 487–501 | DOI | MR | Zbl

[11] Hudson J. F. P., Piecewise Linear Topology, Benjamin, New York–Amsterdam, 1969 | MR | Zbl

[12] Dik T., Gruppy preobrazovanii i teoriya predstavlenii, Mir, M., 1982 | MR

[13] Dranishnikov A. N., “Absolyutnye ekstenzory v razmernosti $n$ i $n$-myagkie otobrazheniya, povyshayuschie razmernost”, UMN, 39:5 (1984), 55–95 | MR | Zbl

[14] Chigogidze A. Ch., “Teoriya $n$-sheipov”, UMN, 44:5 (1988), 117–140 | MR

[15] Jaworowski J., “An equivariant extension theorem and $G$-retracts with a finite structure”, Manuscr. Math., 35 (1981), 323–329 | DOI | MR | Zbl