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Embedding problems related to asymptotic dimension in coarse geometry

Research Project

Project/Area Number 24540099
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Geometry
Research InstitutionWaseda University

Principal Investigator

Koyama Akira  早稲田大学, 理工学術院, 教授 (40116158)

Co-Investigator(Kenkyū-buntansha) EDA Katsuya  早稲田大学, 理工学術院, 教授 (90015826)
Co-Investigator(Renkei-kenkyūsha) CHINEN Naotsugu  防衛大学校, 教授 (20370067)
HOSAKA Tetsuya  静岡大学, 総合科学技術研究科, 准教授 (50344908)
YAGASAKI Tatsuhiko  京都工芸繊維大学, 工芸科学研究科, 教授 (40191077)
Project Period (FY) 2012-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords位相幾何学 / 幾何学的トポロジー / coarse幾何学 / asymptotic次元論 / 埋蔵問題 / 幾何学 / asymptotic次元 / 国際情報交換 / 国際情報研究 / 国際研究者交流 / coarse幾何 / 国際研究者交流(ポーランド) / 国際情報交換(ポーランド)
Outline of Final Research Achievements

We investigated large scale geometry, mainly coarse geometry for general proper metric spaces with coarse geometry structure and embedding problems of CAT(0)-groups into the Hilbert space. Then we discovered a good relation between coarse geometry and small scale geometry which is an ordinal geometric topology. I obtained many interesting results with the collaborators, Jozef Kransinkiewicz and Stanislaw Spiez (the Institute of Mathematic, Polish Academy of Science). Our papers have excellent evaluation and we were invited important international conferences of geometric topology. For example, Dubrovnik VIII-Geometric Group Theory and Dynamical Systems, Dubrovnik, Croatia. It is one of traditional and important topology conferences.
Due to our proposal we organized an international meeting of coarse geometry at Wasoeda University. The future speakers are Jerzy Dydak (University of Tennessee, USA)and Stanislaw Spiez. It was a good occasion to exchange hot results and opinions.

Report

(5 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (11 results)

All 2015 2014 2013 2012 Other

All Int'l Joint Research (2 results) Journal Article (2 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 2 results,  Acknowledgement Compliant: 1 results) Presentation (4 results) (of which Int'l Joint Research: 2 results,  Invited: 3 results) Book (3 results)

  • [Int'l Joint Research] テネシー大学(米国)

    • Related Report
      2015 Annual Research Report
  • [Int'l Joint Research] ポーランド科学アカデミー数学研究所(ポーランド)

    • Related Report
      2015 Annual Research Report
  • [Journal Article] Surfaces in products of two curves2015

    • Author(s)
      A. Koyama, J. Krasinkiewicz and S. Spiez
    • Journal Title

      Topology and its Applications

      Volume: 196

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Embeddings into products and symmetric products - an algebraic approach2012

    • Author(s)
      A. Koyama, J. Krasinkiewicz and S. Spiez
    • Journal Title

      Houston Journal of Mathematics

      Volume: 38 Pages: 611-641

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] A role of Whyburn Factorization Theorem in Dimension Theory2015

    • Author(s)
      A. Koyama
    • Organizer
      The 1st Pan Pacific International Conference on Topology and its Applications
    • Place of Presentation
      Minnan Normal University, Zhang Zhou, China
    • Year and Date
      2015-11-26
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Characterization of n-dimensional compacta in the product of n curves2015

    • Author(s)
      A. Koyama
    • Organizer
      DubrovnikVIII - Geometric Topology, Geometric Group Theory and Dynamical Systems
    • Place of Presentation
      Inter-University Center, Dubrovnik, Croatia
    • Year and Date
      2015-06-22
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On embeddings into products of curves2013

    • Author(s)
      Koyama, Akira
    • Organizer
      28th Summer Conference on Topology and its Applications
    • Place of Presentation
      Nipissing University (Ontario, Canada)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Surfaces in products of two curves2013

    • Author(s)
      Koyama, Akira
    • Organizer
      International Conference on Topology and Geometry 2013
    • Place of Presentation
      Shimane University
    • Related Report
      2013 Research-status Report
  • [Book] Topics in dimension theory, Recent progress in general topology. III2014

    • Author(s)
      J. Dydak and A. Koyama
    • Total Pages
      39
    • Publisher
      Atlantis Press
    • Related Report
      2014 Research-status Report
  • [Book] Topoic in Dimension Theory in "Recent Progress in Topology III"2014

    • Author(s)
      J.Dydak and A. Koyama
    • Total Pages
      39
    • Publisher
      Atlantis Press
    • Related Report
      2013 Research-status Report
  • [Book] Topoic in Dimension Theory in "Recent Progress in Topology"2013

    • Author(s)
      J. Dydak and A. Koyama
    • Total Pages
      39
    • Publisher
      Springer-Verlag
    • Related Report
      2012 Research-status Report

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Published: 2013-05-31   Modified: 2022-02-03  

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