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

• Project/Area Number: 18740029
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Geometry
• Research Institution: The 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: ¥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。

Research Products

• [Journal Article] Lens space surgeries as A'Campo's divide knots (2009)
  • Author(s): Yuichi YAMADA
  • Journal Title: Algebraic & Geometric Topology 電子版 9 Pages: 397-428
  • Peer Reviewed
• [Journal Article] Lens space surgeries as A'Campo's divide knots (2009)
  • Author(s): Yuichi YAMADA
  • Journal Title: Algebraic & Geometric Topology (掲載内定) Pages: 397-428
  • Peer Reviewed
• [Journal Article] Generalized rational blow-down, torus knots, and Euclidean Algorithm (2008)
  • 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
• [Journal Article] Generalized rational blow-down, torus knots, and Euclidean Algorithm (2008)
  • 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
• [Journal Article] A deformation of the Alexander polynomials of knots yielding Lens spaces (2007)
  • Author(s): T.KADOKAMI and Y.YAMADA
  • Journal Title: Bulletin of Australian Mathematics Society 75 Pages: 75-89
  • Peer Reviewed
• [Journal Article] A deformation of the Alexander polynomials of knots yielding Lens spaces (2007)
  • Author(s): T. KADOKAMI and Y. YAMADA
  • Journal Title: Bulletin of Australian Mathematics Society 75 Pages: 75-89
  • Peer Reviewed
• [Journal Article] A deformation of the Alexander polynomials of knots yielding Lens spaces (2007)
  • Author(s): T.KADOKAMI, Y.YAMADA
  • Journal Title: Bulletin of Australian Mathematics Society (掲載予定)(or later)
• [Journal Article] Finite Dehn surgery along A'Campo's divide knots (2006)
  • Author(s): Yuichi YAMADA
  • Journal Title: Advanced Studies in Pure Mathematics 43 Pages: 573-583
  • Peer Reviewed
• [Journal Article] Berge's lens surgeries as A'Campo's divide knots (2006)
  • 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
• [Journal Article] Lens space surgeries and plane curves (2006)
  • 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
• [Journal Article] Reidemeister Torsion and Lens surgeries on (-2,m,n)-Pretzel knots (2006)
  • Author(s): T.KADOKAMI and Y.YAMADA
  • Journal Title: KOBE Journal of Mathematics 23・1-2 Pages: 65-78
  • NAID: 110007030836
  • Peer Reviewed
• [Journal Article] Finite Dehn surgery along A' Campo' s divide knots (2006)
  • Author(s): Yuichi YAMADA
  • Journal Title: Advanced Studies in Pure Mathematics 43 43 Pages: 573-583
• [Journal Article] Berge' s lens surgeries as A' Campo' sdivide knots (2006)
  • 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
• [Journal Article] Lens space surgeries and plane curves (2006)
  • 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
• [Journal Article] Reidemeister Torsion and Lens surgeries on (-2, m, n)-Pretzel knots (2006)
  • Author(s): T.KADOKAMI, Y.YAMADA
  • Journal Title: KOBE Journal of Mathematics 23・1-2 Pages: 65-78
  • NAID: 110007030836
• [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
  • Peer Reviewed
• [Presentation] Dehn surgery along A'Campo's divide knots,Lens spaces and plane curves (2009)
  • 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
• [Presentation] Dehn surgery along A'Campo's divide knots, Lens spaces and plane curves (2009)
  • Author(s): Yuichi YAMADA
  • Organizer: Branched Coverings, Degenerations, and Related Topics
  • Place of Presentation: 広島大学
  • Year and Date: 2009-03-09
• [Presentation] Lens space surgery along A'Campo's divide knots II (2009)
  • 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
• [Presentation] Lens space surgery along A'Campo's divide knots II (2009)
  • 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
• [Presentation] Generalized rational blow-down, torus knots,and Euclidean Algorithm (2008)
  • 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
• [Presentation] Generalized rational blow-down, torus knots, and Euclidean Algorithm (2008)
  • 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
• [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
• [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
• [Presentation] Generalized rational blow-down and Euclidean Algorithm (2007)
  • 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
• [Presentation] Generalized rational blow-down and Euclidean Algorithm (2007)
  • 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
• [Presentation] Kirby Calc (2007)
  • 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
• [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
• [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
• [Presentation] Alexander polynomials of knots repre sented by L-shaped plane curves (2006)
  • 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
• [Presentation] L型平面曲線, Blow-down とDehn surgery I, II (2006)
  • 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
• [Presentation] Berge's lens surgeries as A'Campo's divide knots (2006)
  • 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
• [Remarks] ホームページ等
  • URL: http://matha.e-one.uec.ac.jp/~yyyamada/index.html
• [Remarks]
  • URL: http://matha.e-one.uec.ac.jp/~yyyamada/
• [Remarks]
  • URL: http://matha.e-one.uec.ac.jp/~yyyamada/indexj.html