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Computational topology on knots and spatial graphs

Research Project

Project/Area Number 21500022
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Fundamental theory of informatics
Research InstitutionChuo University

Principal Investigator

YAMAMOTO Makoto  中央大学, 理工学部, 教授 (10158305)

Co-Investigator(Kenkyū-buntansha) HARA Masao  東海大学, 理学部, 准教授 (10238165)
谷 聖一  日本大学, 文理学部, 教授 (70266708)
Co-Investigator(Renkei-kenkyūsha) TANI Seiichi  日本大学, 文理学部, 教授 (70266708)
Project Period (FY) 2009 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywords計算量理論 / 結び目 / 絡み目 / 位相不変量 / Jones多項式 / 計算量 / アルゴリズム
Research Abstract

In this research we obtained the followings ; We showed that our algorithm in 2007 computes Jones polynomials of some kinds of links in O(n^2) time, and that there are infinitely many pairs of alternating pretzel knots whose Jones polynomials are identical though whose knot types are different.

Report

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

    (4 results)

All 2012 2010 2009 Other

All Journal Article (2 results) Presentation (2 results)

  • [Journal Article] O(n^2) time algorithms for computing Jones polynomials of certain links2010

    • Author(s)
      Masahiko Murakami, Masao Hara, Seiichi Tani, Makoto Yamamoto
    • Journal Title

      研究集会「結び目の数学II」報告集

    • Related Report
      2011 Final Research Report
  • [Journal Article] On Jones polynomials of alternating pretzel knot(preprint)

    • Author(s)
      Masao. Hara, Makoto Yamamoto
    • Related Report
      2011 Final Research Report
  • [Presentation] On Jones polynomials of alternating pretzel knots2012

    • Author(s)
      原正雄, 山本慎
    • Organizer
      研究集会「結び目理論の展望」
    • Place of Presentation
      早稲田大学
    • Year and Date
      2012-03-18
    • Related Report
      2011 Annual Research Report 2011 Final Research Report
  • [Presentation] O(n^2) time algorithms for computing Jones polynomials of certain links2009

    • Author(s)
      村上雅彦, 原正雄, 谷聖一, 山本慎
    • Organizer
      研究集会「結び目の数学II」
    • Place of Presentation
      早稲田大学
    • Year and Date
      2009-12-23
    • Related Report
      2011 Final Research Report 2009 Annual Research Report

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

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