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Study on periodic elements in the homotopy groups of spheres

Research Project

Project/Area Number 22740045
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Geometry
Research InstitutionTokyo City University

Principal Investigator

NAKAI Hirofumi  東京都市大学, 知識工学部, 准教授 (80343739)

Project Period (FY) 2010 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2012: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords球面の安定ホモトピー群 / Adams-Novikov スペクトル系列 / 有限CWスペクトラム / Adams-Novikovスペクトル系列
Research Abstract

We obtain some results on triviality and non-triviality of δ -elements in the Adams-Novikov E2-terms, using the module structures of some chromatic E1-terms. And we give some insights on the computability in the motivic Brown-Peterson theory, and on the fiber sequence related to GHMR-resolution of L2-localized sphere spetrcum, which is conjectured by Behrens and Ormsby.

Report

(4 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (15 results)

All 2013 2012 2011 2010 Other

All Journal Article (4 results) Presentation (8 results) (of which Invited: 2 results) Book (2 results) Remarks (1 results)

  • [Journal Article] ラムダ代数を用いたAdamsE2項の元の表示2013

    • Author(s)
      中井洋史
    • Journal Title

      東京都市大学共通教育センター紀要

      Volume: 6 Pages: 81-93

    • Related Report
      2012 Final Research Report
  • [Journal Article] ラムダ代数を用いたAdams E2項の元の表示2013

    • Author(s)
      中井洋史
    • Journal Title

      東京都市大学共通教育センター紀要

      Volume: 6 Pages: 81-93

    • Related Report
      2012 Annual Research Report
  • [Journal Article] Motivicホモトピー圏におけるChromatic的手法2012

    • Author(s)
      中井洋史
    • Journal Title

      東京都市大学共通教育センター紀要

      Volume: 5 Pages: 43-56

    • NAID

      40019298841

    • Related Report
      2012 Final Research Report 2011 Annual Research Report
  • [Journal Article] トポロジーの工学への応用(現状と展望)2011

    • Author(s)
      中井洋史
    • Journal Title

      東京都市大学共通教育センター紀要

      Volume: 4 Pages: 91-103

    • NAID

      40018813064

    • Related Report
      2012 Final Research Report 2010 Annual Research Report
  • [Presentation] Adams型のスペクトル系列「(コ)ホモロジーからホモトピーへの架け橋」「解決した問題,未解決の問題」2013

    • Author(s)
      中井洋史
    • Organizer
      代数的トポロジー信州春の学校
    • Place of Presentation
      信州大学
    • Year and Date
      2013-03-10
    • Related Report
      2012 Final Research Report
  • [Presentation] Behrens'Q(N) spectra and Shimomura's β -elements2012

    • Author(s)
      中井洋史
    • Organizer
      高知ホモトピー論談話会
    • Place of Presentation
      高知大学
    • Year and Date
      2012-12-28
    • Related Report
      2012 Final Research Report
  • [Presentation] Exact Functor theorems and Elliptic cohomologies2012

    • Author(s)
      中井洋史
    • Organizer
      SGAD2012
    • Place of Presentation
      東京大学
    • Year and Date
      2012-11-15
    • Related Report
      2012 Final Research Report
  • [Presentation] Toward understanding the motivic chromatic phenomena2011

    • Author(s)
      中井洋史
    • Organizer
      高知ホモトピー論談話会
    • Place of Presentation
      高知大学
    • Year and Date
      2011-12-28
    • Related Report
      2012 Final Research Report 2011 Annual Research Report
  • [Presentation] On p-torsion δ-elements in the Adams-Novikov spectral sequence2010

    • Author(s)
      中井洋史,加藤諒
    • Organizer
      日本数学会秋期会トポロジー分科会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-24
    • Related Report
      2012 Final Research Report
  • [Presentation] On p-torsion δ-elements in the Adams-Novikov spectral sequence2010

    • Author(s)
      中井洋史(加藤諒氏と共同)
    • Organizer
      日本数学会秋期会トポロジー分科会
    • Place of Presentation
      名古屋大学(愛知)
    • Year and Date
      2010-09-24
    • Related Report
      2010 Annual Research Report
  • [Presentation] Exact functor theorems and Elliptic cohomologies

    • Author(s)
      中井洋史
    • Organizer
      SGAD2012
    • Place of Presentation
      東京大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Behrens’ Q(N) spectra and Shimomura’s β-elements

    • Author(s)
      中井洋史
    • Organizer
      高知ホモトピー論談話会
    • Place of Presentation
      高知大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Book] 世界を読み解くリテラシー2011

    • Author(s)
      井上健・山本史華・中井洋史
    • Publisher
      萌書房
    • Related Report
      2012 Final Research Report
  • [Book] 世界を読み解くリテラシー2011

    • Author(s)
      井上健・山本史華・中井洋史(共編)
    • Total Pages
      272
    • Publisher
      萌書房
    • Related Report
      2010 Annual Research Report
  • [Remarks]

    • URL

      http://www.comm.tcu.ac.jp/~math/hnakai/index.html

    • Related Report
      2012 Final Research Report

URL: 

Published: 2010-08-23   Modified: 2019-07-29  

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