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Development and Applications of Arithmetic Topology

Research Project

Project/Area Number 21340010
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionKyushu University

Principal Investigator

MORISHITA Masanori  九州大学, 数理学研究院, 教授 (40242515)

Co-Investigator(Renkei-kenkyūsha) 河野 俊丈  東京大学, 数理科学研究科, 教授
栗原 将人  慶応義塾大学, 理工学部, 教授
坂内 健一  慶応義塾大学, 理工学部, 講師
田口 雄一郎  九州大学, 数理学研究院, 准教授
寺嶋 郁二  東京工業大学, 理工学研究科, 助教
Project Period (FY) 2009 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥6,110,000 (Direct Cost: ¥4,700,000、Indirect Cost: ¥1,410,000)
Fiscal Year 2011: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2010: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2009: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Keywords結び目 / 素数 / 数論的位相幾何学
Research Abstract

Based on the analogies between knots and primes, I found a new branch of mathematics, called arithmetic topology, focused upon the analogies between knot theory and number theory. I wrote a book giving a foundation of this field. As applications, I studied some analogies between 3-dimensional hyperbolic geometry, Chern-Simons theory and Hida theory. I also organized international workshops,“Low dimensional topology and number theory", every year during 2009. 2012.

Report

(4 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (26 results)

All 2012 2011 2010 2009 Other

All Journal Article (7 results) (of which Peer Reviewed: 2 results) Presentation (10 results) Book (5 results) Remarks (4 results)

  • [Journal Article] Analogies between knots and primes, 3-manifolds and number rings2010

    • Author(s)
      M. Morishita
    • Journal Title

      Sugaku Expositions

    • Related Report
      2011 Final Research Report
  • [Journal Article] The universal deformation and the associated homological invariants for hyperbolic knots2010

    • Author(s)
      M. Morishita
    • Journal Title

      Oberwolfach report

    • Related Report
      2011 Final Research Report
  • [Journal Article] Chern-Simons variation and Deligne cohomology, to appear in : Spectral Analysis in Geometry and Number Theory on Prof2009

    • Author(s)
      M. Morishita, Y. Terashima
    • Journal Title

      Toshikazu Sunada' s 60th birthday, Contemporary Math

      Pages: 127-134

    • Related Report
      2011 Final Research Report
  • [Journal Article] 数論と結び目日変量,数理科学2009

    • Author(s)
      森下昌紀
    • Journal Title

      「数学と物理に広がる不変量-量子トポロジーとその周辺」

      Pages: 36-41

    • Related Report
      2011 Final Research Report
  • [Journal Article] Chern-Simons variation and Deligne cohomology2009

    • Author(s)
      M.Monshita, Y.Terashima
    • Journal Title

      Contemporary Mathcmatcs 484

      Pages: 127-134

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 数論的位相幾何学と数論的場の理論

    • Author(s)
      森下昌紀
    • Journal Title

      代数学ミンポジウム報告集

      Volume: (to appear)(掲載確定)

    • Related Report
      2011 Annual Research Report
  • [Journal Article] Analogies between knofs and primes, 3-manfolds and number rings

    • Author(s)
      M.Monshita
    • Journal Title

      Sugaku Expositions (to appears)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Presentation] Knots and Primes2012

    • Organizer
      Tata Institute of Fundamental Research
    • Year and Date
      2012-02-16
    • Related Report
      2011 Final Research Report
  • [Presentation] 結び目と素数-数論的位相幾何学入門2011

    • Organizer
      仙台シンポジウム
    • Place of Presentation
      東北大学
    • Year and Date
      2011-08-25
    • Related Report
      2011 Final Research Report
  • [Presentation] 数論的位相幾何学と数論的場の理論2011

    • Organizer
      代数学シンポジウム
    • Place of Presentation
      岡山大学
    • Year and Date
      2011-08-11
    • Related Report
      2011 Final Research Report
  • [Presentation] 数論的位相幾何学と数論的場の理論2011

    • Author(s)
      森下昌紀
    • Organizer
      代数学ミンポジウム
    • Place of Presentation
      岡山大(招待講演)
    • Year and Date
      2011-08-06
    • Related Report
      2011 Annual Research Report
  • [Presentation] The universal deformation and the associated homological invariants for hyperbolic knots2010

    • Organizer
      Low dimensional topology and number theory
    • Place of Presentation
      Oberwolfach, Germany
    • Year and Date
      2010-08-17
    • Related Report
      2011 Final Research Report 2010 Annual Research Report
  • [Presentation] Lecture on arithmetic topology2010

    • Organizer
      Number Theory Seminar
    • Place of Presentation
      KIAS, Korea
    • Year and Date
      2010-07-15
    • Related Report
      2011 Final Research Report
  • [Presentation] Knots and Primes2010

    • Organizer
      Colloquium and seminars
    • Place of Presentation
      KAIST,韓国
    • Related Report
      2011 Final Research Report
  • [Presentation] Hyperbolic geometry and Hida-Matur theory2010

    • Author(s)
      M.Morishita
    • Organizer
      KAIST Colloguim
    • Place of Presentation
      KAIST(韓国)
    • Related Report
      2009 Annual Research Report
  • [Presentation] The universal deformation and the associated Alexander-Fox invariant2009

    • Organizer
      トポロジー-幾何学セミナー
    • Place of Presentation
      広島大学
    • Year and Date
      2009-11-17
    • Related Report
      2011 Final Research Report
  • [Presentation] 3-dimensional hyperbolic geometry and Hida theory2009

    • Organizer
      East Asia Number Theory Conference
    • Place of Presentation
      Tsinghua University, China
    • Year and Date
      2009-08-22
    • Related Report
      2011 Final Research Report
  • [Book] Knots and Primes-An Introduction to Arithmetic Topology2012

    • Author(s)
      M. Morishita
    • Publisher
      Springer
    • Related Report
      2011 Final Research Report
  • [Book] Knots and Primes-An Introduction to Arithmetic Topology2012

    • Author(s)
      Masanori Morishita
    • Total Pages
      200
    • Publisher
      Springer
    • Related Report
      2011 Annual Research Report
  • [Book] 日本の現代数学-新しい展開をめざして-,結び目と素数-数論的位相幾何学2010

    • Author(s)
      森下昌紀
    • Publisher
      数学書房
    • Related Report
      2011 Final Research Report
  • [Book] 結び目と素数2009

    • Author(s)
      森下昌紀
    • Publisher
      シュプリンガーシャパン
    • Related Report
      2009 Annual Research Report
  • [Book] Knots and Primes-An Introduction to Arithmetic Topology

    • Author(s)
      M.Morishita
    • Total Pages
      200
    • Publisher
      Springer(to appear)
    • Related Report
      2010 Annual Research Report
  • [Remarks] Low dimensional topology and number theory II, 2010, 3月,東京

    • Related Report
      2011 Final Research Report
  • [Remarks] Low dimensional topology and number theory III, 2011, 3月,福岡

    • Related Report
      2011 Final Research Report
  • [Remarks] Low dimensional topology and number theory IV, 2012, 3月,福岡

    • Related Report
      2011 Final Research Report
  • [Remarks]

    • URL

      http://www2.math.kyushu-u.ac.jp/~morisita/workshop.html

    • Related Report
      2011 Final Research Report

URL: 

Published: 2009-04-01   Modified: 2016-04-21  

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