Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Izv. RAN. Ser. Mat., 2012, Volume 76, Issue 5, Pages 3–28 (Mi izv5883)  

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

Isovariant extensors and the characterization of equivariant homotopy equivalences

S. M. Ageev

Belarusian State University, Minsk

Abstract: We extend the well-known theorem of James–Segal to the case of an arbitrary family $\mathcal{F}$ of conjugacy classes of closed subgroups of a compact Lie group $G$: a $G$-map $f\colon\mathbb{X}\to\mathbb{Y}$ of metric $\operatorname{Equiv}_{\mathcal{F}}$-$\mathrm{ANE}$-spaces is a $G$-homotopy equivalence if and only if it is a weak $G$-$\mathcal{F}$-homotopy equivalence. The proof is based on the theory of isovariant extensors, which is developed in this paper and enables us to endow $\mathcal{F}$-classifying $G$-spaces with an additional structure.

Keywords: classifying $G$-spaces, isovariant absolute extensor, weak equivariant homotopy equivalence.

DOI: https://doi.org/10.4213/im5883

Full text: PDF file (690 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2012, 76:5, 857–880

Bibliographic databases:

UDC: 515.124.62+515.122.4
MSC: 54H15, 54E40, 57S10
Received: 15.11.2010
Revised: 14.11.2011

Citation: S. M. Ageev, “Isovariant extensors and the characterization of equivariant homotopy equivalences”, Izv. RAN. Ser. Mat., 76:5 (2012), 3–28; Izv. Math., 76:5 (2012), 857–880

Citation in format AMSBIB
\Bibitem{Age12}
\by S.~M.~Ageev
\paper Isovariant extensors and the characterization of equivariant homotopy equivalences
\jour Izv. RAN. Ser. Mat.
\yr 2012
\vol 76
\issue 5
\pages 3--28
\mathnet{http://mi.mathnet.ru/izv5883}
\crossref{https://doi.org/10.4213/im5883}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3024861}
\zmath{https://zbmath.org/?q=an:1266.54081}
\elib{https://elibrary.ru/item.asp?id=20359145}
\transl
\jour Izv. Math.
\yr 2012
\vol 76
\issue 5
\pages 857--880
\crossref{https://doi.org/10.1070/IM2012v076n05ABEH002607}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000310548800001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84868096252}


Linking options:
  • http://mi.mathnet.ru/eng/izv5883
  • https://doi.org/10.4213/im5883
  • http://mi.mathnet.ru/eng/izv/v76/i5/p3

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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, D. D. Repovš, “The Covering Homotopy Extension Problem for Compact Transformation Groups”, Math. Notes, 92:6 (2012), 737–750  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. S. M. Ageev, “On Palais universal $G$-spaces and isovariant absolute extensors”, Sb. Math., 203:6 (2012), 769–797  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. Ageev S., Usimov I., “The cohomology ring of subspaces of universal $S^1$-space with finite orbit types”, Topology Appl., 160:11 (2013), 1255–1260  crossref  mathscinet  zmath  isi  scopus
    4. I. V. Usimov, “Zapirayuschie kogomologii 3-mernogo tora”, Tr. In-ta matem., 22:2 (2014), 84–95  mathnet
    5. I. V. Usimov, “Algebras of the equivariant cohomologies of an $\mathfrak F$-classifying $T^k$-spaces”, Russian Math. (Iz. VUZ), 59:1 (2015), 51–59  mathnet  crossref
    6. S. M. Ageev, “On the exponent of $G$-spaces and isovariant extensors”, Sb. Math., 207:2 (2016), 155–190  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. 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
    8. West J., “Involutions of Hilbert Cubes That Are Hyperspaces of Peano Continua”, Topology Appl., 240 (2018), 238–248  crossref  mathscinet  zmath  isi  scopus
    9. Bykov A., Texis M., “Isovariant Fibrant Spaces”, Topology Appl., 264 (2019), 322–335  crossref  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:566
    Full text:121
    References:54
    First page:14

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2022