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

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

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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

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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• http://mi.mathnet.ru/eng/msb8463
• https://doi.org/10.4213/sm8463
• http://mi.mathnet.ru/eng/msb/v207/i2/p3

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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
2. J. West, “Involutions of Hilbert cubes that are hyperspaces of Peano continua”, Topology Appl., 240 (2018), 238–248
3. I. Belegradek, “Hyperspaces of smooth convex bodies up to congruence”, Adv. Math., 332 (2018), 176–198
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