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Comprehensive Study on Applications of CWL Invariants

Research Project

Project/Area Number 16K05158
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Geometry
Research InstitutionMusashino Art University

Principal Investigator

Maruyama Noriko  武蔵野美術大学, 造形学部, 教授 (80147008)

Project Period (FY) 2016-04-01 – 2020-03-31
Project Status Completed (Fiscal Year 2019)
Budget Amount *help
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords3次元多様体 / 位相不変量 / デデキント和 / キャッソンウォーカー不変量 / レスコップ不変量 / ライデマイスタートウラエフ不変量 / 有理ホモロジー3球面 / デーン手術 / 有理ホモロジー球面 / キャッソン不変量 / ウォーカー不変量 / ライデマイスター不変量 / 幾何学 / 低次元多様体論
Outline of Final Research Achievements

In the four years of the adoption period (2016-2019 including extension of one year), the objective of this comprehensive study on the Casson-Walker-Lescop (CWL) invariant for rational homology 3-spheres were the following three. (1) Continued research on the CWL invariants so far, (2) Validation of the effectiveness of applying the CWL invariants in combination with the Reidemister-Turaev torsion on rational homology 3-spheres and (3) Specific studies with a view to the relationship with other invariants such as the Seiberg-Witten invariants. She conducted research on describing geometric phenomena via the CWL invariant and published four papers in professional journals and one university research bulletin. In addition to making public announcements and making oral presentations at research meetings, we also hold research meetings with researchers in similar research fields to make oral presentations.

Academic Significance and Societal Importance of the Research Achievements

専門学術雑誌に公表した本研究成果では、CWL不変量の計算の主要部分であるデデキント和の計算法や振動する値を不等式で評価する方法の提案やどのように応用するのかの着眼点に学術的意義がある。例えば、双曲結び目から手術によって有限群位数のホモロジー群を持った有理ホモロジーレンズ空間が得られるのは有限個であるなど、既存の複雑な議論で得られた結果について粗いがCWL不変量が有限性を捕捉していること、有理ホモロジーレンズ空間の絡み形式に相当する不変量の組がCWL不変量の小数部分から得られること等があり、これからこの不変量について研究する若い研究者への布石として社会的意義があると考えられる。

Report

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

    (7 results)

All 2019 2018 2017 2016

All Journal Article (6 results) (of which Peer Reviewed: 5 results,  Acknowledgement Compliant: 1 results) Presentation (1 results)

  • [Journal Article] A bound for the Casson-Walker invariant of rational homology null cobordant lens spaces2019

    • Author(s)
      Noriko Maruyama
    • Journal Title

      Topology and Its Application

      Volume: 265 Pages: 1-14

    • DOI

      10.1016/j.topol.2019.106822

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The CWL invariant and surgeries along 2-components links III2018

    • Author(s)
      Noriko Maruyama
    • Journal Title

      武蔵野美術大学研究紀要

      Volume: 49

    • Related Report
      2018 Research-status Report
  • [Journal Article] Seifer surgery on knots via Reidemister torsion and Casson-Walker-Lescop invariant III2018

    • Author(s)
      Teruhisa Kadokami, Noriko Maruyama, Tsuyoshi Sakai
    • Journal Title

      Topology and its Applications

      Volume: 248 Pages: 78-81

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] A distribution of rational homology 3-spheres captured bby the CWL invariant Phase 12017

    • Author(s)
      Noriko Maruyama
    • Journal Title

      Journal of Knot Theory and Its Ramifications

      Volume: 26 Pages: 1-19

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] Seifert surgery on knots via Reidemister torsion and Casson-Walker-Lescop invariant II2016

    • Author(s)
      T. Kadokami, N. Maruyama, T. Sakai
    • Journal Title

      Osaka J. Math.

      Volume: 53 Pages: 767-773

    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] Some arithmetic properties of the CWL invariant2016

    • Author(s)
      N. Maruyama
    • Journal Title

      Top. Appl.

      Volume: 206 Pages: 115-125

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] A bound for the Casson-Walker invariant of rational homology null cobordant lens spaces2019

    • Author(s)
      円山 憲子
    • Organizer
      北陸結び目セミナー
    • Related Report
      2019 Annual Research Report

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Published: 2016-04-21   Modified: 2021-02-19  

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