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Study on the homotopy types of polyhedral products

Research Project

Project/Area Number 26400094
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Geometry
Research InstitutionOsaka Prefecture University

Principal Investigator

Iriye Kouyemon  大阪府立大学, 理学(系)研究科(研究院), 教授 (40151691)

Co-Investigator(Kenkyū-buntansha) 岸本 大祐  京都大学, 理学研究科, 准教授 (60402765)
蓮井 翔  筑波大学, 数理物質系, 助教 (50792454)
Project Period (FY) 2014-04-01 – 2020-03-31
Project Status Completed (Fiscal Year 2019)
Budget Amount *help
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords単体複体 / Golod 性 / 多面体積 / モーメントアングル複体 / Massey 積 / ホモトピー型 / ポストニコフ分解 / 非輪状 / 旗複体 / 殻化可能複体 / ホワイトヘッド積 / Golod性 / Massey積 / 球面の三角形分割 / 連結和 / polyhedral product / Golodness / Cohen-Macaulay complex / high neighborly complex
Outline of Final Research Achievements

In 2004 Baskakov-Buchstaber-Panov showed that it is possible to study Golodness of a simplicial complex through the study of the homotopy type of its moment-angle complex.
We have studied the homotopy types of polyhdedral products, which are a generalization of moment-angle complexes, to study Golodness of a simplicial complex by making use of the result above.
In particular, we showed that the moment-angle complex associated with a dual shellable complex is homotopy equivalent to a suspension space. We also constructed a moment-angle complex associated with a Golod simplicial complex which is not homotopy equivalent to a suspension space.

Academic Significance and Societal Importance of the Research Achievements

数学の果たしている社会的役割は、諸科学に言葉と手段を提供することにあります。本研究はトポロジーという分野に属する研究ですが、この分野が生まれてから100年経ってようやく具体的な応用分野が生まれました。それは、トポロジカルデータアナリシスという統計とは全く異なる方法でデータを解析する手段です。
本研究は、空間内の点のつながりを抽象化したグラフ(ネットワーク図のようなもの)をさらに抽象化した単体複体から構成される図形の研究に関するものです。これは、現在行われているトポロジカルデータアナリシスの方法と類似しており、その方面への応用が期待されています。

Report

(7 results)
  • 2019 Annual Research Report   Final Research Report ( PDF )
  • 2018 Research-status Report
  • 2017 Research-status Report
  • 2016 Research-status Report
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (21 results)

All 2021 2020 2019 2018 2017 2016 2015 2014

All Journal Article (8 results) (of which Peer Reviewed: 8 results,  Open Access: 1 results,  Acknowledgement Compliant: 2 results) Presentation (13 results) (of which Int'l Joint Research: 3 results,  Invited: 9 results)

  • [Journal Article] Whitehead products in moment-angle complexes2021

    • Author(s)
      Kouyemon Iiriye and Daisuke Kishomoto
    • Journal Title

      Journal of th Mathematical Society of Japan

      Volume: 印刷中

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Relative phantom maps2019

    • Author(s)
      K. Iriye, D. Kishimoto, and T. Matsushita
    • Journal Title

      Algebr. Geom. Topol.

      Volume: 19 Issue: 1 Pages: 341-362

    • DOI

      10.2140/agt.2019.19.341

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] Fat wedge filtrations and decomposition of polyhedral products2019

    • Author(s)
      K. Iriye and D. Kishimoto
    • Journal Title

      Kyoto J. Math.

      Volume: 59 Issue: 1 Pages: 1-51

    • DOI

      10.1215/21562261-2017-0038

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] On the moment-angle manifold constructed by Fan, Chen, Ma and Wang2018

    • Author(s)
      Kouyemon Iriye
    • Journal Title

      Osaka Journal of Mathematics

      Volume: 55 Pages: 587-593

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Golodness and polyhedral products for two dimensional simplicial complexes2018

    • Author(s)
      Kouyemon Iriye, Daisuke Kishimoto
    • Journal Title

      Forum Mathematics

      Volume: 30 Issue: 2 Pages: 527-532

    • DOI

      10.1515/forum-2017-0130

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] A Golod complex with non-suspension moment-angle complex2017

    • Author(s)
      Kouyemon Iriye and Tatusya Yano
    • Journal Title

      Topology and its Applications

      Volume: 225 Pages: 145-163

    • DOI

      10.1016/j.topol.2017.04.027

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] Fat wedge filtration and decomposition of polyhedral products2017

    • Author(s)
      Kouyemon Iriye and Daisuke Kishomoto
    • Journal Title

      Kyoto Journal of Mathematics

      Volume: 印刷中

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Decomposition of suspension of spaces involving polyhedral products2016

    • Author(s)
      Kouyemon Iriye and Daisuke Kishomoto
    • Journal Title

      Algebraic & Geometric Topology

      Volume: 16 Issue: 2 Pages: 825-841

    • DOI

      10.2140/agt.2016.16.825

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] Golodness and polyhedral products for surface triangulation2020

    • Author(s)
      岸本大佑
    • Organizer
      Toric Topology Research Seminar. the Fields Institute for Research in Mathematial Sciences
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] When is a polyhedral product a finite Postnikov section?2020

    • Author(s)
      岸本大佑
    • Organizer
      Workshop on polyhedral products in Homotopy Theorey
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Higher Whitehead products in moment-angle complexes2019

    • Author(s)
      岸本大佑
    • Organizer
      Toric Topology 2019 in Okayama
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] Whitehead products in moment-angle complexes2019

    • Author(s)
      岸本大祐
    • Organizer
      福岡ホモトピー論セミナー
    • Related Report
      2018 Research-status Report
  • [Presentation] Golod 性とその周辺2018

    • Author(s)
      入江幸右衛門
    • Organizer
      ホモトピー沖縄
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] Right-angled Coxeter quandles and polyhedral products2018

    • Author(s)
      岸本大祐
    • Organizer
      ホモトピー論シンポジウム2018
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] The Stanley-Reisner functor for a poset2018

    • Author(s)
      岸本大祐
    • Organizer
      離散幾何構造セミナー
    • Related Report
      2018 Research-status Report
  • [Presentation] ポリヘドラル・プロダクトのホモトピー論2018

    • Author(s)
      岸本大祐
    • Organizer
      2018 日本数学会 年会
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] Homotopy theory of polyhedral products2017

    • Author(s)
      入江幸右衛門
    • Organizer
      ホモトピー論シンポジウム
    • Related Report
      2017 Research-status Report
  • [Presentation] Homotopy decomposition of diagonal arrangements2016

    • Author(s)
      岸本大祐
    • Organizer
      Toric Topology Workshop
    • Place of Presentation
      大阪市立大学
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] ポリヘドラルプロダクトのホモトピー論2016

    • Author(s)
      岸本大祐
    • Organizer
      第63回トポロジーシンポジウム
    • Place of Presentation
      神戸大学
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] On a polyhedral product which is homotopy equivalent to a suspension space2015

    • Author(s)
      入江幸右衛門
    • Organizer
      Workshop and Seminar on Topological Combinatorics
    • Place of Presentation
      タイ(KASETSART大学)
    • Year and Date
      2015-01-05 – 2015-01-09
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] On a Golod conjecture2014

    • Author(s)
      入江幸右衛門
    • Organizer
      ホモトピー論シンポジウム
    • Place of Presentation
      大阪府立大学
    • Year and Date
      2014-11-01 – 2014-11-03
    • Related Report
      2014 Research-status Report

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Published: 2014-04-04   Modified: 2021-02-19  

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