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Study of exceptional surgeries on 3-manifolds from the singularity theory

Research Project

Project/Area Number 18740029
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Geometry
Research InstitutionThe University of Electro-Communications

Principal Investigator

YAMADA Yuichi  The University of Electro-Communications, 電気通信学部, 准教授 (30303019)

Project Period (FY) 2006 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥3,930,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥330,000)
Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2007: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2006: ¥1,300,000 (Direct Cost: ¥1,300,000)
Keywords位相幾何 / 特異点 / 3次元多様体 / デーン手術 / 4次元多様体 / 結び目 / 特異点論 / 枠付き絡み目 / レンズ空間 / 平面曲線 / 特異点諭 / 伜付き絡み目
Research Abstract

3次元球面内の結び目に沿うデーン手術(Dehn surgery)でレンズ空間が生じる"例外的"な現象は「レンズ手術」と呼ばれ、低次元多様体論の研究課題となっている。本研究では「いくつかのレンズ手術は特異点論に由来したdivide knot であり、対応する平面曲線は『L 型』の領域に沿って斜めの格子を切り取った形状をしている」という現象とその関連話題に取り組み、論文や講演で報告した。

Report

(4 results)
  • 2008 Annual Research Report   Final Research Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • Research Products

    (35 results)

All 2009 2008 2007 2006 Other

All Journal Article (16 results) (of which Peer Reviewed: 7 results) Presentation (16 results) Remarks (3 results)

  • [Journal Article] Lens space surgeries as A'Campo's divide knots2009

    • Author(s)
      Yuichi YAMADA
    • Journal Title

      Algebraic & Geometric Topology 電子版 9

      Pages: 397-428

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Lens space surgeries as A'Campo's divide knots2009

    • Author(s)
      Yuichi YAMADA
    • Journal Title

      Algebraic & Geometric Topology (掲載内定)

      Pages: 397-428

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Generalized rational blow-down, torus knots, and Euclidean Algorithm2008

    • Author(s)
      山田 裕一
    • Journal Title

      日本数学会 秋季総合分科会トポロジー分科会 アブストラクト

      Pages: 50-51

    • Related Report
      2008 Final Research Report
  • [Journal Article] Generalized rational blow-down, torus knots, and Euclidean Algorithm2008

    • Author(s)
      山田裕一
    • Journal Title

      日本数学会秋季総合分科会トポロジー分科会アブストラクト

      Pages: 83-84

    • Related Report
      2008 Annual Research Report
  • [Journal Article] A deformation of the Alexander polynomials of knots yielding Lens spaces2007

    • Author(s)
      T.KADOKAMI and Y.YAMADA
    • Journal Title

      Bulletin of Australian Mathematics Society 75

      Pages: 75-89

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A deformation of the Alexander polynomials of knots yielding Lens spaces2007

    • Author(s)
      T. KADOKAMI and Y. YAMADA
    • Journal Title

      Bulletin of Australian Mathematics Society 75

      Pages: 75-89

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A deformation of the Alexander polynomials of knots yielding Lens spaces2007

    • Author(s)
      T.KADOKAMI, Y.YAMADA
    • Journal Title

      Bulletin of Australian Mathematics Society (掲載予定)(or later)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Finite Dehn surgery along A'Campo's divide knots2006

    • Author(s)
      Yuichi YAMADA
    • Journal Title

      Advanced Studies in Pure Mathematics 43

      Pages: 573-583

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Berge's lens surgeries as A'Campo's divide knots2006

    • Author(s)
      山田 裕一
    • Journal Title

      2006年度 日本数学会 秋季総合分科会トポロジー分科会 アブストラクト

      Pages: 83-8

    • Related Report
      2008 Final Research Report
  • [Journal Article] Lens space surgeries and plane curves2006

    • Author(s)
      山田 裕一
    • Journal Title

      研究集会「結び目のトポロジーVIII」報告集

      Pages: 51-64

    • Related Report
      2008 Final Research Report
  • [Journal Article] Reidemeister Torsion and Lens surgeries on (-2,m,n)-Pretzel knots2006

    • Author(s)
      T.KADOKAMI and Y.YAMADA
    • Journal Title

      KOBE Journal of Mathematics 23・1-2

      Pages: 65-78

    • NAID

      110007030836

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Finite Dehn surgery along A' Campo' s divide knots2006

    • Author(s)
      Yuichi YAMADA
    • Journal Title

      Advanced Studies in Pure Mathematics 43 43

      Pages: 573-583

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Berge' s lens surgeries as A' Campo' sdivide knots2006

    • Author(s)
      山田裕一
    • Journal Title

      日本数学会 秋季総合分科会 トポロジー分科会アプストラクト

      Pages: 83-84

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Lens space surgeries and plane curves2006

    • Author(s)
      山田裕一
    • Journal Title

      研究集会「結び目のトポロジーVIII」報告集

      Pages: 51-64

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Reidemeister Torsion and Lens surgeries on (-2, m, n)-Pretzel knots2006

    • Author(s)
      T.KADOKAMI, Y.YAMADA
    • Journal Title

      KOBE Journal of Mathematics 23・1-2

      Pages: 65-78

    • NAID

      110007030836

    • Related Report
      2006 Annual Research Report
  • [Journal Article] A note on essential tori in the exterior of torus knots with twists

    • Author(s)
      K.MORIMOTO and Y.YAMADA
    • Journal Title

      KOBE Journal of Mathematics

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Presentation] Dehn surgery along A'Campo's divide knots,Lens spaces and plane curves2009

    • Author(s)
      Yuichi YAMADA
    • Organizer
      研究集会 Branched Coverings, Degenerations, and Related Topics
    • Place of Presentation
      広島大学
    • Year and Date
      2009-03-09
    • Related Report
      2008 Final Research Report
  • [Presentation] Dehn surgery along A'Campo's divide knots, Lens spaces and plane curves2009

    • Author(s)
      Yuichi YAMADA
    • Organizer
      Branched Coverings, Degenerations, and Related Topics
    • Place of Presentation
      広島大学
    • Year and Date
      2009-03-09
    • Related Report
      2008 Annual Research Report
  • [Presentation] Lens space surgery along A'Campo's divide knots II2009

    • Author(s)
      Yuichi YAMADA
    • Organizer
      The 5th East Asian School of Knots and Related Topics
    • Place of Presentation
      慶州教育文化会館(慶州,韓国)
    • Year and Date
      2009-01-12
    • Related Report
      2008 Final Research Report
  • [Presentation] Lens space surgery along A'Campo's divide knots II2009

    • Author(s)
      Yuichi YAMADA
    • Organizer
      The 5th East Asian School of Knots and Related Tonics
    • Place of Presentation
      慶州教育文化会館(韓国)
    • Year and Date
      2009-01-12
    • Related Report
      2008 Annual Research Report
  • [Presentation] Generalized rational blow-down, torus knots,and Euclidean Algorithm2008

    • Author(s)
      山田 裕一
    • Organizer
      日本数学会 秋季総合分科会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-25
    • Related Report
      2008 Final Research Report
  • [Presentation] Generalized rational blow-down, torus knots, and Euclidean Algorithm2008

    • Author(s)
      山田裕一
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-25
    • Related Report
      2008 Annual Research Report
  • [Presentation] Torus knots, generalized rational blow-down, and lens space surgery of Type 7, 82008

    • Author(s)
      Yuichi YAMADA
    • Organizer
      研究集会「4次元のトポロジー」
    • Place of Presentation
      広島大学
    • Year and Date
      2008-02-07
    • Related Report
      2008 Final Research Report
  • [Presentation] Torus knots, generalized rational blow-down, and lens space surgery of Type 7,8.2008

    • Author(s)
      Yuichi YAMADA
    • Organizer
      研究集会「4次元のトポロジー」
    • Place of Presentation
      広島大学
    • Year and Date
      2008-02-07
    • Related Report
      2007 Annual Research Report
  • [Presentation] Generalized rational blow-down and Euclidean Algorithm2007

    • Author(s)
      山田 裕一
    • Organizer
      入門(解説)研究集会「低次元幾何学 と 無限次元幾何学」
    • Place of Presentation
      東京大学玉原国際セミナーハウス
    • Year and Date
      2007-09-12
    • Related Report
      2008 Final Research Report
  • [Presentation] Generalized rational blow-down and Euclidean Algorithm2007

    • Author(s)
      山田 裕一
    • Organizer
      「低次元幾何学と無限次元幾何学」
    • Place of Presentation
      東京大学 玉原国際セミナーハウス
    • Year and Date
      2007-09-12
    • Related Report
      2007 Annual Research Report
  • [Presentation] Kirby Calc2007

    • Author(s)
      山田 裕一
    • Organizer
      入門(解説)研究集会「低次元幾何学 と 無限次元幾何学」
    • Place of Presentation
      東京大学玉原国際セミナーハウス
    • Year and Date
      2007-09-11
    • Related Report
      2008 Final Research Report
  • [Presentation] 多様体の中で具体的にキャッソンハンドルを"作る"2007

    • Author(s)
      山田 裕一
    • Organizer
      「キャッソンハンドル勉強会」
    • Place of Presentation
      東京大学玉原国際セミナーハウス
    • Year and Date
      2007-05-27
    • Related Report
      2008 Final Research Report
  • [Presentation] 多様体の中で具体的にキヤツソンハンドルを″作る″2007

    • Author(s)
      山田 裕一
    • Organizer
      「キヤッソンハンドル勉強会」
    • Place of Presentation
      東京大学 玉原国際セミナーハウス
    • Year and Date
      2007-05-27
    • Related Report
      2007 Annual Research Report
  • [Presentation] Alexander polynomials of knots repre sented by L-shaped plane curves2006

    • Author(s)
      Yuichi YAMADA(部分的に 門上晃久氏との共同研究)
    • Organizer
      研究集会「トポロジーとコンピュータ2006」
    • Place of Presentation
      大阪産業大学梅田サテライト
    • Year and Date
      2006-11-28
    • Related Report
      2008 Final Research Report
  • [Presentation] L型平面曲線, Blow-down とDehn surgery I, II2006

    • Author(s)
      山田 裕一
    • Organizer
      Workshop「不変量を用いない結び目理論」
    • Place of Presentation
      箱根高原ホテル
    • Year and Date
      2006-11-05
    • Related Report
      2008 Final Research Report
  • [Presentation] Berge's lens surgeries as A'Campo's divide knots2006

    • Author(s)
      山田 裕一
    • Organizer
      日本数学会 秋季総合分科会
    • Place of Presentation
      大阪市立大学
    • Year and Date
      2006-09-21
    • Related Report
      2008 Final Research Report
  • [Remarks] ホームページ等

    • URL

      http://matha.e-one.uec.ac.jp/~yyyamada/index.html

    • Related Report
      2008 Final Research Report
  • [Remarks]

    • URL

      http://matha.e-one.uec.ac.jp/~yyyamada/

    • Related Report
      2008 Annual Research Report
  • [Remarks]

    • URL

      http://matha.e-one.uec.ac.jp/~yyyamada/indexj.html

    • Related Report
      2007 Annual Research Report

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Published: 2006-04-01   Modified: 2016-04-21  

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