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



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Zametki, 2011, Volume 90, Issue 2, Pages 300–305 (Mi mz8732)  

This article is cited in 7 scientific papers (total in 7 papers)

Toral Rank Conjecture for Moment-Angle Complexes

Yu. M. Ustinovskii

M. V. Lomonosov Moscow State University

Abstract: We consider an operation $K\mapsto L(K)$ on the set of simplicial complexes, which we call the “doubling operation.” This combinatorial operation was recently introduced in toric topology in an unpublished paper of Bahri, Bendersky, Cohen and Gitler on generalized moment-angle complexes (also known as $K$-powers). The main property of the doubling operation is that the moment-angle complex $\mathscr Z_K$ can be identified with the real moment-angle complex $\mathbb R\mathscr Z_{L(K)}$ for the double $L(K)$. By way of application, we prove the toral rank conjecture for the spaces $\mathscr{Z}_K$ by providing a lower bound for the rank of the cohomology ring of the real moment-angle complexes $\mathbb R\mathscr Z_K$. This paper can be viewed as a continuation of the author's previous paper, where the doubling operation for polytopes was used to prove the toral rank conjecture for moment-angle manifolds.

Keywords: moment-angle manifold, moment-angle complex, simplicial complex, doubling, toral rank conjecture, cohomology rank, Mayer–Vietoris sequence

DOI: https://doi.org/10.4213/mzm8732

Full text: PDF file (450 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2011, 90:2, 279–283

Bibliographic databases:

UDC: 515.146.39
Received: 27.01.2010
Revised: 24.10.2010

Citation: Yu. M. Ustinovskii, “Toral Rank Conjecture for Moment-Angle Complexes”, Mat. Zametki, 90:2 (2011), 300–305; Math. Notes, 90:2 (2011), 279–283

Citation in format AMSBIB
\Bibitem{Ust11}
\by Yu.~M.~Ustinovskii
\paper Toral Rank Conjecture for Moment-Angle Complexes
\jour Mat. Zametki
\yr 2011
\vol 90
\issue 2
\pages 300--305
\mathnet{http://mi.mathnet.ru/mz8732}
\crossref{https://doi.org/10.4213/mzm8732}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2918445}
\transl
\jour Math. Notes
\yr 2011
\vol 90
\issue 2
\pages 279--283
\crossref{https://doi.org/10.1134/S0001434611070273}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000294363500027}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-80052067402}


Linking options:
  • http://mi.mathnet.ru/eng/mz8732
  • https://doi.org/10.4213/mzm8732
  • http://mi.mathnet.ru/eng/mz/v90/i2/p300

    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. Yu. M. Ustinovskii, “O pochti svobodnykh deistviyakh tora i gipoteze Khorroksa”, Dalnevost. matem. zhurn., 12:1 (2012), 98–107  mathnet
    2. Yu Li, “Small covers and the Halperin-Carlsson conjecture”, Pacific J. Math., 256:2 (2012), 489–507  crossref  mathscinet  zmath  isi  scopus
    3. Bahri A., Bendersky M., Cohen F.R., Gitler S., “Operations on Polyhedral Products and a New Topological Construction of Infinite Families of Toric Manifolds”, Homol. Homotopy Appl., 17:2 (2015), 137–160  crossref  mathscinet  zmath  isi  scopus
    4. Cho H.W., “Periodicity and the values of the real Buchstaber invariants”, J. Math. Soc. Jpn., 68:4 (2016), 1695–1723  crossref  mathscinet  zmath  isi  scopus
    5. Park H., “Wedge Operations and Doubling Operations of Real Toric Manifolds”, Chin. Ann. Math. Ser. B, 38:6 (2017), 1321–1334  crossref  mathscinet  zmath  isi  scopus
    6. Vidaurre E., “On Polyhedral Product Spaces Over Polyhedral Joins”, Homol. Homotopy Appl., 20:2 (2018), 259–280  crossref  mathscinet  zmath  isi  scopus
    7. Yu L., “On Free Z(P)-Torus Actions in Dimensions Two and Three”, Sci. China-Math., 62:2 (2019), 391–410  crossref  mathscinet  zmath  isi  scopus
  • Математические заметки Mathematical Notes
    Number of views:
    This page:310
    Full text:60
    References:46
    First page:18

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019