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Izv. Akad. Nauk SSSR Ser. Mat., 1988, Volume 52, Issue 1, Pages 212–228 (Mi izv1176)  

This article is cited in 9 scientific papers (total in 9 papers)

On free actions of zero-dimensional compact groups

A. N. Dranishnikov


Abstract: It is proved that there exists a free action of an arbitrary zero-dimensional compact group on every Menger manifold. It is shown that in the case of a finite group $G$ such a $G$-action on the $n$-dimensional Menger compactum is unique and universal in the class of free $G$-actions on $n$-dimensional compacta.
Bibliography: 22 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1989, 32:1, 217–232

Bibliographic databases:

UDC: 515.12
MSC: Primary 57S10, 22C05, 22E35; Secondary 54F45, 54D30, 54H15, 54E60
Received: 07.02.1986

Citation: A. N. Dranishnikov, “On free actions of zero-dimensional compact groups”, Izv. Akad. Nauk SSSR Ser. Mat., 52:1 (1988), 212–228; Math. USSR-Izv., 32:1 (1989), 217–232

Citation in format AMSBIB
\Bibitem{Dra88}
\by A.~N.~Dranishnikov
\paper On~free actions of zero-dimensional compact groups
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1988
\vol 52
\issue 1
\pages 212--228
\mathnet{http://mi.mathnet.ru/izv1176}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=936531}
\zmath{https://zbmath.org/?q=an:0689.57025|0648.57016}
\transl
\jour Math. USSR-Izv.
\yr 1989
\vol 32
\issue 1
\pages 217--232
\crossref{https://doi.org/10.1070/IM1989v032n01ABEH000755}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. M. Ageev, “Classification of $G$-spaces”, Russian Acad. Sci. Izv. Math., 41:3 (1993), 581–591  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. S. M. Ageev, “Classifying spaces for free actions, and the Hilbert–Smith conjecture”, Russian Acad. Sci. Sb. Math., 75:1 (1993), 137–144  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. D. Repovš, A. B. Skopenkov, E. V. Ščepin, “Group actions on manifolds and smooth ambient homogeneity”, J Math Sci, 83:4 (1994), 546  crossref
    4. S. M. Ageev, “A characterization of the free actions of zero-dimensional compact groups on $k$-dimensional Menger compacta”, Izv. Math., 59:2 (1995), 229–270  mathnet  crossref  mathscinet  zmath  isi
    5. Yutaka Iwamoto, “Fixed point sets of transformation groups of Menger manifolds, their pseudo-interiors and their pseudo-boundaries”, Topology and its Applications, 68:3 (1996), 267  crossref
    6. Thierry Giordano, Pierre de la Harpe, “Moyennabilité des groupes dénombrables et actions sur les espaces de Cantor”, Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 324:11 (1997), 1255  crossref
    7. D. Repovš, A. B. Skopenkov, E. V. Ščepin, “Group actions on manifolds and smooth ambient homogeneity”, J Math Sci, 83:4 (1997), 546  crossref
    8. A.N. Dranishnikov, “Boundaries of Coxeter groups and simplicial complexes with given links”, Journal of Pure and Applied Algebra, 137:2 (1999), 139  crossref
    9. Zhiqing Yang, “A construction of classifying spaces for p-adic group actions”, Topology and its Applications, 153:1 (2005), 161  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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