Exceptional surgeries of 3-manifolds and strange 4-manifolds

• Project/Area Number: 21540072
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: The University of Electro-Communications
• Principal Investigator: YAMADA Yuichi 電気通信大学, 大学院・情報理工学研究科, 教授 (30303019)
• Co-Investigator(Kenkyū-buntansha): HIROSE Susumu 東京理科大学, 理工学部, 准教授 (10264144) ; YAMAGUCHI Kohhei 電気通信大学, 大学院・情報理工学研究科, 教授 (00175655) ; OHNO Masahiro 電気通信大学, 大学院・情報理工学研究科, 准教授 (70277820)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000); 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: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: 3次元多様体 / 4次元多様体 / レンズ空間 / デーン手術 / 枠付き絡み目 / カービー計算 / 平面曲線 / divide knot / Kirby計算 / 特異点論

Research Abstract

Phenomenon that a Dehn surgery along a(hyperbolic) knot in the 3-sphere yields alensspace is called "lens space surgery" and is a subject in low-dimensional topology. Concerned with a question "Can we construct strange 4-manifolds by lens space surgeries?", I wrote two papers as jointworks : Torsion invariants related to lens space surgery. Pairs of distinct knots yielding same lens spaces.

Research Products

• [Journal Article] On diffeomorphisms over nonorientable surfaces standardly embedded in the 4-sphere (2012)
  • Author(s): S. Hirose
  • Journal Title: Algebraic & Geometric Topology Volume: 12 Pages: 109130-109130
  • Peer Reviewed
• [Journal Article] Twisted topological invariants and topology of low-dimensional manifolds (2011)
  • Author(s): T. Kadokamiand Y. Yamada
  • Journal Title: RIMS合宿型セミナー報告集 Volume: 12 Pages: 67-76
  • URL: http://www.kurims.kyoto-u.ac.jp/.kyodo/kokyuroku/contents/1747.html
• [Journal Article] Spaces of algebraic maps and continuous maps between real algebraic varieties (2011)
  • Author(s): M. Adamszek, A. Kozlowski and K. Yamaguchi
  • Journal Title: Quart. J. Math. Volume: 62-4 Pages: 771-790
  • Peer Reviewed
• [Journal Article] Lens space surgeries along two component links, and Reidemeister-Turaev torsion (2011)
  • Author(s): KADOKAMI Teruhisa, YAMADA Yuichi
  • Journal Title: 数理解析研究所講究録「Twisted topological invariants and topology of low-dimensional manifolds」 Volume: 1747 Pages: 67-76
• [Journal Article] Four dimensional manifolds constructed by lens space surgeries along torus knots (2011)
  • Author(s): 丹下基生, 山田裕一
  • Journal Title: 日本数学会2011年度年会(震災のため中止)トポロジー分科会講演アブストラクト Pages: 33-34
  • NAID: 120007137182
• [Journal Article] Canonical forms of the knots in the genus one fiber surfaces (2010)
  • Author(s): Y. Yamada
  • Journal Title: Bulletin of the University of Electro-Communications Volume: 22-1 Pages: 25-31
  • Peer Reviewed
• [Journal Article] Spaces of algebraic maps from real projective spaces into complex projective spaces (2010)
  • Author(s): A. Kozlowski and K. Yamaguchi
  • Journal Title: Contemporary Math Volume: 519 Pages: 145-164
  • Peer Reviewed
• [Journal Article] Realization of the mapping class group of handlebody by diffeomorphisms (2010)
  • Author(s): S. Hirose
  • Journal Title: Proceedings of the American Math. Soc Volume: 138 Pages: 4157-4159
  • Peer Reviewed
• [Journal Article] Canonical forms of the knots in the genus one fiber surfaces (2010)
  • Author(s): Yuichi YAMADA
  • Journal Title: 電気通信大学紀要 Volume: 22-1 Pages: 25-31
• [Journal Article] Canonical forms of the knots in the genus one fiber surfaces (2010)
  • Author(s): Yuichi YAMADA
  • Journal Title: Bulletin of the University of Electro-Communications 22-1 Pages: 25-31
  • Peer Reviewed
• [Journal Article] Lens space surgeries along certain 2-component links and Reidemeister-Turaev torsion (2010)
  • Author(s): 門上晃久, 山田裕一
  • Journal Title: 日本数学会2010年度年会,トポロジー分科会 講演アブストラクト Pages: 82-83
• [Journal Article] Lens space surgeries as A Campo's divide knots (2009)
  • Author(s): Y. Yamada
  • Journal Title: Algebraic & Geometric Topology Volume: 9 Issue: 1 Pages: 397-428
  • DOI: 10.2140/agt.2009.9.397
  • Peer Reviewed
• [Journal Article] A note on essential tori in theexterior of torus knots with twists (2009)
  • Author(s): K. Morimoto and Y. Yamada
  • Journal Title: Kobe J. of Math Volume: 261-2 Pages: 29-34
  • Peer Reviewed
• [Journal Article] Lens space surgeries as A'Campo's divide knots (2009)
  • Author(s): Yuichi YAMADA
  • Journal Title: Algebraic & Geometric Topology 9 Pages: 397-428
  • Peer Reviewed
• [Journal Article] A note on essential tori in the exterior of torus knots with twists (2009)
  • Author(s): Kanji MORIMOTO, Yuichi YAMADA
  • Journal Title: Kobe J.of Math. 261-2 Pages: 29-34
  • Peer Reviewed
• [Presentation] 4-manifolds constructed by lens space surgery (2012)
  • Author(s): 山田裕一
  • Organizer: 上正明氏のセミナー
  • Place of Presentation: 京都大学
• [Presentation] 4-manifolds constructed by lens space surgery (2012)
  • Author(s): 丹下基生、山田裕一
  • Organizer: 京都大学上教授のセミナー
  • Place of Presentation: 京都大学大学院理学研究科
• [Presentation] Simplicial resolutions and their related topics (2011)
  • Author(s): 山口耕平
  • Organizer: 城崎ホモトピー論研究集会
  • Place of Presentation: 城崎福祉会館
  • Year and Date: 2011-11-04
• [Presentation] レンズ空間手術から構成する4次元多様体 (2011)
  • Author(s): 山田裕一
  • Organizer: 広島大学トポロジー・幾何セミナー
  • Place of Presentation: 広島大学
  • Year and Date: 2011-07-05
• [Presentation] レンズ空間手術から構成する4次元多様体 (2011)
  • Author(s): 丹下基生、山田裕一
  • Organizer: 広島大学トポロジー・幾何セミナー
  • Place of Presentation: 広島大学理学部(招待)
  • Year and Date: 2011-07-05
• [Presentation] Truncated simplicial resolutions andspaces of algebraicaps (2011)
  • Author(s): 山口耕平
  • Organizer: RIMS研究集会「変換群の幾何と組み合わせ論」
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2011-06-15
• [Presentation] Four dimensional manifolds constructed Four dimensional manifolds constructed by lens space surgeries along torus knots (2011)
  • Author(s): 山田裕一
  • Organizer: 日本数学会年会トポロジー分科会
  • Place of Presentation: 早稲田大学
  • Year and Date: 2011-03-20
• [Presentation] Lens space surgeries along certain 2-component links, and Reidemeister-Turaev torsion (2010)
  • Author(s): 山田裕一
  • Organizer: RIMS合宿型セミナー
  • Place of Presentation: あきた白神体験センター
  • Year and Date: 2010-09-16
• [Presentation] Lens space surgeries along certain 2-component links, and Reidemeister-Turaev torsion (2010)
  • Author(s): 山田裕一
  • Organizer: Twisted topological invariants and topology of low-dimensional manifolds
  • Place of Presentation: あきた白神体験センター
  • Year and Date: 2010-09-16
• [Presentation] Divide knot presentation of Berge's knots of lens space surgery (2010)
  • Author(s): Yuichi YAMADA
  • Organizer: 研究集会
  • Place of Presentation: Univ. of Burgundy Dijon(FRANCE)
  • Year and Date: 2010-09-07
• [Presentation] Divide knot presentation of Berge's knots of lens space surgery (2010)
  • Author(s): Yuichi YAMADA
  • Organizer: Singularities, knots, and mapping class groups in memory of Bernard Perron
  • Place of Presentation: Bourgogne Univ., Dijon(France)
  • Year and Date: 2010-09-07
• [Presentation] Spaces of Z/2-equivariant maps between some real algebraic varieties (2010)
  • Author(s): 山口耕平
  • Organizer: RIMS研究集会変換群と手術理論
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2010-08-31
• [Presentation] The homotopy of spaces of algebraic maps between real algebraic varieties (2010)
  • Author(s): 山口耕平
  • Organizer: RIMS研究集会
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2010-06-29
• [Presentation] Lens space surgeries along certain 2-component links and Reidemeister-Turaev torsion (2010)
  • Author(s): 山田裕一
  • Organizer: 日本数学会年会トポロジー分科会
  • Place of Presentation: 慶応大学理工学部
  • Year and Date: 2010-03-26
• [Presentation] Lens space surgeries along certain 2-component links and Reidemeister-Turaev torsion (2010)
  • Author(s): 門上晃久, 山田裕一
  • Organizer: 日本数学会2010年度年会,トポロジー分科会
  • Place of Presentation: 慶応義塾大学
  • Year and Date: 2010-03-26
• [Presentation] The homotopy type of spaces of algebraic mapsI (2010)
  • Author(s): M. Adamaszek, A. Kozlowski and K. Yamaguchi
  • Organizer: 日本数学会年会トポロジー分科会
  • Place of Presentation: 慶応大学理工学部
  • Year and Date: 2010-03-25
• [Presentation] The homotopy type of spaces of algebraic mapsII (2010)
  • Author(s): M. Adamaszek, A. Kozlowski and K. Yamaguchi
  • Organizer: 日本数学会年会トポロジー分科会
  • Place of Presentation: 慶応大学理工学部
  • Year and Date: 2010-03-25
• [Presentation] Every Berge's knot of lens space surgery is a divide knot (2010)
  • Author(s): Yuichi YAMADA
  • Organizer: The sixth East Asian School of Knots and Related topics
  • Place of Presentation: 南開大学
  • Year and Date: 2010-01-28
• [Presentation] Every Berge' s knot of lens space surgery is a divide knot (2010)
  • Author(s): Yuichi YAMADA
  • Organizer: The sixth East Asian School of Knots and Related Topics
  • Place of Presentation: 南開大学Chern Inst.(中国, 天津)
  • Year and Date: 2010-01-28
• [Presentation] フリードマン原論文に学ぶ (2009)
  • Author(s): 山田裕一
  • Organizer: キャッソン・フリードマン理論研究会
  • Place of Presentation: けいはんなプラザ(京都)
  • Year and Date: 2009-10-19
• [Presentation] フリードマン原論文に学ぶ 6章, 8章 (2009)
  • Author(s): 山田裕一
  • Organizer: キャッソン・フリードマン理論 研究会
  • Place of Presentation: 京都 けいはんなプラザホテル
  • Year and Date: 2009-10-19
• [Presentation] 4次元多様体を表す Kirby Diagram (2009)
  • Author(s): 山田裕一
  • Organizer: 基礎から応用
  • Place of Presentation: 筑波大学トポロジーセミナー
  • Year and Date: 2009-10-01
• [Presentation] 4次元多様体を表すKirby Diagram:基礎から応用 (2009)
  • Author(s): 山田裕一
  • Organizer: 筑波大学トポロジーセミナー
  • Place of Presentation: 筑波大学 自然系学棟
  • Year and Date: 2009-10-01
• [Remarks]
  • URL: http://matha.e-one.uec.ac.jp/.yyyamada/indexj.html
• [Remarks]
  • URL: http://matha.e-one.uec.ac.jp/~yyyamada/indexj.html
• [Remarks]
  • URL: http://matha.a-one.uec.ac.jp/~yyyamada/indexj.html
• [Remarks]
  • URL: http://matha.e-one.uec.ac.jp/~yyyamada/indexj.html