Uspekhi Matematicheskikh Nauk
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Subscription
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Uspekhi Mat. Nauk:
Year:
Volume:
Issue:
Page:
Find






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


Uspekhi Mat. Nauk, 2016, Volume 71, Issue 2(428), Pages 3–80 (Mi umn9704)  

This article is cited in 10 scientific papers (total in 10 papers)

Homotopy theory in toric topology

J. Grbić, S. Theriault

University of Southampton, Southampton, UK

Abstract: In toric topology one associates with each simplicial complex $K$ on $m$ vertices two key spaces, the Davis–Januszkiewicz space $DJ_{K}$ and the moment-angle complex $\mathscr{Z}_{K}$, which are related by a homotopy fibration $\mathscr{Z}_{K}\xrightarrow{\widetilde{w}}DJ_K\to \prod_{i=1}^{m}\mathbb{C}P^{\infty}$. A great deal of work has been done to study the properties of $DJ_{K}$ and $\mathscr{Z}_{K}$, their generalizations to polyhedral products, and applications to algebra, combinatorics, and geometry. Chap. 1 surveys some of the main results in the homotopy theory of these spaces. Chap. 2 breaks new ground by initiating a study of the map $\widetilde{w}$. It is shown that, for a certain family of simplicial complexes $K$, the map $\widetilde{w}$ is a sum of higher and iterated Whitehead products.
Bibliography: 49 titles.

Keywords: Davis–Januszkiewicz space, moment-angle complex, polyhedral product, homotopy type, higher Whitehead product, higher Samelson product.

DOI: https://doi.org/10.4213/rm9704

Full text: PDF file (1125 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2016, 71:2, 185–251

Bibliographic databases:

UDC: 515.1
MSC: 55Pxx, 55Q15, 57N65
Received: 16.04.2015

Citation: J. Grbić, S. Theriault, “Homotopy theory in toric topology”, Uspekhi Mat. Nauk, 71:2(428) (2016), 3–80; Russian Math. Surveys, 71:2 (2016), 185–251

Citation in format AMSBIB
\Bibitem{GrbThe16}
\by J.~Grbi{\'c}, S.~Theriault
\paper Homotopy theory in toric topology
\jour Uspekhi Mat. Nauk
\yr 2016
\vol 71
\issue 2(428)
\pages 3--80
\mathnet{http://mi.mathnet.ru/umn9704}
\crossref{https://doi.org/10.4213/rm9704}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3507473}
\zmath{https://zbmath.org/?q=an:1346.55014}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2016RuMaS..71..185G}
\elib{https://elibrary.ru/item.asp?id=25865516}
\transl
\jour Russian Math. Surveys
\yr 2016
\vol 71
\issue 2
\pages 185--251
\crossref{https://doi.org/10.1070/RM9704}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000380765700001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84979900458}


Linking options:
  • http://mi.mathnet.ru/eng/umn9704
  • https://doi.org/10.4213/rm9704
  • http://mi.mathnet.ru/eng/umn/v71/i2/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. T. E. Panov, Ya. A. Veryovkin, “Polyhedral products and commutator subgroups of right-angled Artin and Coxeter groups”, Sb. Math., 207:11 (2016), 1582–1600  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. I. Limonchenko, “Topology of moment-angle manifolds arising from flag nestohedra”, Chin. Ann. Math. Ser. B, 38:6 (2017), 1287–1302  crossref  mathscinet  zmath  isi  scopus
    3. J. Grbić, M. Intermont, I. Laude, E. Vidaurre, “A homotopy theoretical generalisation of the Bestvina-Brady construction”, Topology Appl., 235 (2018), 43–53  crossref  mathscinet  zmath  isi  scopus
    4. S. Theriault, “Toric homotopy theory”, Combinatorial and toric homotopy, Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap., 35, World Sci. Publ., Hackensack, NJ, 2018, 1–66  mathscinet  zmath  isi
    5. S. A. Abramyan, “Iterated higher Whitehead products in topology of moment-angle complexes”, Siberian Math. J., 60:2 (2019), 185–196  mathnet  crossref  crossref  isi  elib
    6. T. Panov, S. Theriault, “The homotopy theory of polyhedral products associated with flag complexes”, Compos. Math., 155:1 (2019), 206–228  crossref  mathscinet  isi
    7. V. M. Buchstaber, I. Yu. Limonchenko, “Massey products, toric topology and combinatorics of polytopes”, Izv. Math., 83:6 (2019), 1081–1136  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    8. Semyon A. Abramyan, Taras E. Panov, “Higher Whitehead Products in Moment–Angle Complexes and Substitution of Simplicial Complexes”, Proc. Steklov Inst. Math., 305 (2019), 1–21  mathnet  crossref  crossref  mathscinet  isi  elib
    9. Ivan Yu. Limonchenko, “On Higher Massey Products and Rational Formality for Moment–Angle Manifolds over Multiwedges”, Proc. Steklov Inst. Math., 305 (2019), 161–181  mathnet  crossref  crossref  mathscinet  isi  elib
    10. K. Iriye, D. Kishimoto, “Whitehead products in moment-angle complexes”, J. Math. Soc. Jpn., 72:4 (2020), 1239–1257  crossref  mathscinet  zmath  isi
  • Успехи математических наук Russian Mathematical Surveys
    Number of views:
    This page:577
    Full text:142
    References:66
    First page:62

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021