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Mat. Sb., 2016, Volume 207, Number 2, Pages 3–44 (Mi msb8463)  

This article is cited in 3 scientific papers (total in 3 papers)

On the exponent of $G$-spaces and isovariant extensors

S. M. Ageev

Belarusian State University, Minsk, Belarus

Abstract: The equivariant version of the Curtis-Schori-West theorem is investigated. It is proved that for a nondegenerate Peano $G$-continuum $\mathbb X$ with an action of the compact abelian Lie group $G$, the exponent $\exp\mathbb X$ is equimorphic to the maximal equivariant Hilbert cube if and only if the free part $\mathbb X_{\mathrm{free}}$ is dense in $\mathbb X$. We also show that the latter is sufficient for the equimorphy of $\exp\mathbb X$ and $\mathbb Q$ in the case of an action of an arbitrary compact Lie group $G$. The key to the proof of these results lies in the theory of the universal $G$-space (in the sense of Palais).
Bibliography: 28 titles.

Keywords: isovariant absolute extensor, Palais universal $G$-space, classifying $G$-space, exponent of $G$-space, equivariant Hilbert cube.

Funding Agency Grant Number
Ministry of Education of the Republic of Belarus
This paper was written with the partial support of a grant from the Ministry of Education of the Republic of Belarus.


DOI: https://doi.org/10.4213/sm8463

Full text: PDF file (842 kB)
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English version:
Sbornik: Mathematics, 2016, 207:2, 155–190

Bibliographic databases:

UDC: 515.124.62+515.122.4
MSC: 54C15, 54C20, 54C55, 54H15, 55R91
Received: 29.12.2014 and 20.07.2015

Citation: S. M. Ageev, “On the exponent of $G$-spaces and isovariant extensors”, Mat. Sb., 207:2 (2016), 3–44; Sb. Math., 207:2 (2016), 155–190

Citation in format AMSBIB
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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, “On a Classifying Property of Regular Representations”, Funct. Anal. Appl., 50:4 (2016), 248–256  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. J. West, “Involutions of Hilbert cubes that are hyperspaces of Peano continua”, Topology Appl., 240 (2018), 238–248  crossref  mathscinet  zmath  isi  scopus
    3. I. Belegradek, “Hyperspaces of smooth convex bodies up to congruence”, Adv. Math., 332 (2018), 176–198  crossref  mathscinet  zmath  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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