Non-hyperbolic Dehn surgeries on hyperbolic knots

• Project/Area Number: 17540097
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: Nihon University
• Principal Investigator: MOTEGI Kimihiko Nihon University, 文理学部, 教授 (40219978)
• Project Period (FY): 2005 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥3,320,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥420,000); Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2007: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2006: ¥600,000 (Direct Cost: ¥600,000); Fiscal Year 2005: ¥900,000 (Direct Cost: ¥900,000)
• Keywords: Dehn surgery / Seifert fiber space / hyperbolic knot / Seifert Surgery Network / Seifert fiber spac / lens space / seiferter / closed geodesic / Deh surgery / network

Research Abstract

本研究では、非双曲Dehn手術のうち、Seifert手術-Seifert多様体を生成する手術-に焦点を絞り、Seifert手術がどのように生じるのか、その"発生のしくみ"を明らかにすることを目標に研究を進めてきた。ある結び目のDehn手術でSeifert多様体が生じた際、"なぜ"その結び目がSeifert手術を許容しているのか、その発生の原因をSeifert Surgery Networkとよばれるネットワークを導入することにより、Seifert手術の遺伝性という新たな視点で捉えることが可能となった。

Research Products

• [Journal Article] Networking Seifert surgeries on knots II : Berge's lens surgeries (2009)
  • Author(s): A. Deruelle, K. Miyazaki and K. Motegi
  • Journal Title: Topology Appl 156 Pages: 1083-1113
  • Peer Reviewed
• [Journal Article] Hyperbolic sections in Seifert fibered surface bundles (2009)
  • Author(s): Kazuhiro Ichihara
  • Journal Title: Quart. J. Math. Oxford Ser. (2)出版受理 (印刷中)
  • Peer Reviewed
• [Journal Article] Band sum operations yielding trivial knots (2009)
  • Author(s): Kai Ishihara
  • Journal Title: Boletin de la Sociedad Matematica Mexicana 出版受理 (印刷中)
  • Peer Reviewed
• [Journal Article] Networking Seifert Surgeries on Knots ll : The Berge's lens surgeries (2009)
  • Author(s): Arnaud Deruelle
  • Journal Title: Topology Appl. 156 Pages: 1083-1113
  • Peer Reviewed
• [Journal Article] Seifert Fibered Slopes and Boundary Slopes on Small Hyperbolic Knots (2008)
  • Author(s): K. Ichihara and K. Motegi
  • Journal Title: Knots, Bull. Nara Univ. Ed. Natur. Sci. 57 Pages: 21-25
  • NAID: 120001075914
  • Peer Reviewed
• [Journal Article] Seifert Fibered Slopes and Boundary Slopes on Small Hyperbolic Knots (2008)
  • Author(s): Kazuhiro Ichihara
  • Journal Title: Bull. Nara Univ. Ed. Natur. Sci. 57 Pages: 21-25
  • Peer Reviewed
• [Journal Article] Hyperbolic sections in surface bundles (2007)
  • Author(s): K. Ichihara and K. Motegi
  • Journal Title: Topology Appl. 154 Pages: 1398-1406
  • Peer Reviewed
• [Journal Article] Hyperbolic sections in surface bundles (2007)
  • Author(s): Kazuhiro Ichihara
  • Journal Title: Topology Appl. 154 Pages: 1398-1406
  • Peer Reviewed
• [Journal Article] Networking Seifert Surgeries on Knots II: The Berge's lens surgeries (2007)
  • Author(s): Arnaud Deruell
  • Journal Title: Topology Appl. 出版受理
  • Peer Reviewed
• [Journal Article] Seifert fibered surgeries which do not arise from primitive/Seifert-fibered constructions (2006)
  • Author(s): T. Mattman, K. Miyazaki and K. Motegi
  • Journal Title: Trans. Amer. Math. Soc. 358 Pages: 4045-4055
  • Peer Reviewed
• [Journal Article] Geometric types of twisted knots (2006)
  • Author(s): M. AitNouh, D. Matignon and K. Motegi
  • Journal Title: Ann. Math. Blaise Pascal 13 Pages: 31-85
  • Peer Reviewed
• [Journal Article] Seifert fibered surgeries which do not arise from primitive/Seifert-fibered constructions constructions (2006)
  • Author(s): Thomas Mattman
  • Journal Title: Trans. Amer. Math. Soc. 358 Pages: 4045-4055
• [Journal Article] Geometric types of twisted knots (2006)
  • Author(s): Mohamed Ait Nouh
  • Journal Title: Ann. Math. Blaise Pascal 13 Pages: 31-85
• [Journal Article] All integral slopes can be Seifert fibered slopes for hyperbolic knots (2005)
  • Author(s): H.-J. Song and K. Motegi
  • Journal Title: Algebr. Geom. Topol. 5 Pages: 369-378
  • Peer Reviewed
• [Journal Article] Braids and Nielsen-Thurston types of automorphisms of punctured surface (2005)
  • Author(s): K. Ichihara and K. Motegi
  • Journal Title: Tokyo J. Math. 28 Pages: 527-538
  • Peer Reviewed
• [Journal Article] On primitive/Seifert-fibered constructions (2005)
  • Author(s): K. Miyazaki and K. Motegi
  • Journal Title: Math. Proc. Camb. Phil. Soc. 138 Pages: 421-435
  • Peer Reviewed
• [Journal Article] Obtaining graph knots by twisting unknots (2005)
  • Author(s): M. AitNouh, D. Matignon and K. Motegi
  • Journal Title: Topology Appl. 146-147 Pages: 105-121
  • Peer Reviewed
• [Journal Article] All integral slopes can be Seifert fibered slopes for hyperbolic knots (2005)
  • Author(s): Hyun-Jong Song, Kimihiko Motegi
  • Journal Title: Algebraic and Geometric Topology 5 Pages: 369-378
• [Journal Article] On primitive/Seifert-fibered constructions (2005)
  • Author(s): Katura Miyazaki, Kimihiko Motegi
  • Journal Title: Math.Proc.Camb.Phill.Soc. 138 Pages: 421-435
• [Journal Article] Braids and Nielsen-Thurston types of automorphisms of punctured surface (2005)
  • Author(s): Kazuhiro Ichihara, Kimihiko Motegi
  • Journal Title: Tokyo J.Math. 28 Pages: 527-538
• [Journal Article] Band sum operations yielding trivial knots
  • Author(s): K. Ishihara and K. Motegi
  • Journal Title: Boletin de la Sociedad Matematica Mexicana (出版受理)
  • Peer Reviewed
• [Journal Article] Hyperbolic sections in Seifert fibered surface bundles
  • Author(s): K. Ichihara and K. Motegi
  • Journal Title: Quart. J. Math. Oxford Ser (2)(出版受理)
  • Peer Reviewed
• [Journal Article] Hyperbolic sections in surface bundles
  • Author(s): Kazuhiro Ichihara
  • Journal Title: Topology Appl. 印刷中
• [Journal Article] Seifert fibered surgeries which do not arise from primitive/Seifert-fibered constructions
  • Author(s): Thomas Mattman, Katura Miyazaki, Kimihiko Motegi
  • Journal Title: Trans.Amer.Math.Soc. (印刷中)
• [Journal Article] Geometric types of twisted knots
  • Author(s): Mohamed Ait Nouh, Daniel Matignon, Kimihiko Motegi
  • Journal Title: Ann.Math.Blaise Pascal (出版受理)
• [Presentation] Seifert surgeries on knots and their network (2009)
  • Author(s): K. Motegi
  • Organizer: Knots in Washington XXVII
  • Place of Presentation: George Washington University
  • Year and Date: 2009-01-11
• [Presentation] Spreaders of Seifert surgeries on knots (2008)
  • Author(s): K. Motegi
  • Organizer: Intelligence of Low Dimensional Topology
  • Place of Presentation: 大阪市立大学
  • Year and Date: 2008-10-07
• [Presentation] Spreaders of Seifert surgeries on knots (2008)
  • Author(s): 茂手木公彦
  • Organizer: Intelligence of Low Dimens ional Topology
  • Place of Presentation: 大阪市立大学
  • Year and Date: 2008-10-07
• [Presentation] Networking Seifert surgeries on knots (2008)
  • Author(s): K. Motegi
  • Organizer: Topology Seminar
  • Place of Presentation: Universite de Nantes
  • Year and Date: 2008-03-06
• [Presentation] Networking Seifert surgeries on knots (2008)
  • Author(s): K. Motegi
  • Organizer: GT3 Seminar Institute de Recherche Mathematique Avancee (IRMA)
  • Place of Presentation: Universite Louis Pasteur
  • Year and Date: 2008-03-03
• [Presentation] " Seifert surgeryのなすネットワークの解明をめざして I " " Seifert surgeryのなすネットワークの解明をめざして II " (2008)
  • Author(s): K. Motegi
  • Organizer: 第2回福岡・札幌幾何学セミナー
  • Place of Presentation: 九州大学
• [Presentation] Seifert surgeryのなすネットワークの解明をめざしてI、II (2008)
  • Author(s): 茂手木 公彦
  • Organizer: 第2回福岡・札幌幾何学セミナー
  • Place of Presentation: 九州大学
• [Presentation] Networking Seifert surgeries on knots (2007)
  • Author(s): K. Motegi
  • Organizer: UNAM Topology Seminar
  • Place of Presentation: Institute of Mathematics National Autonomous University of Mexico (UNAM)
  • Year and Date: 2007-11-22
• [Presentation] Networking Seifert surgeries on knots (2007)
  • Author(s): K. Motegi
  • Organizer: UT Topology Seminar
  • Place of Presentation: The University of Texas at Austin
  • Year and Date: 2007-09-17
• [Presentation] Networking Seifert surgeries on knots (2006)
  • Author(s): 茂手木公彦
  • Organizer: 第53回トポロジーシンポジウム
  • Place of Presentation: 大阪市立大学
  • Year and Date: 2006-08-08
• [Presentation] Seifert fibered surgeriesのネットワーク (2006)
  • Author(s): 茂手木公彦
  • Organizer: 近畿大学数学講演会
  • Place of Presentation: 近畿大学
  • Year and Date: 2006-07-13
• [Presentation] ようこそSeifert surgeryの森へ (2006)
  • Author(s): 茂手木公彦
  • Organizer: 早稲田大学教育学部トポロジーセミナー
  • Place of Presentation: 早稲田大学
  • Year and Date: 2006-06-24
• [Presentation] Networking Seifert Surgeries on Knots (2006)
  • Author(s): K. Motegi
  • Organizer: Knots, Groups and 3-Manifolds in Marseille 2006
  • Place of Presentation: Universite de Provence
  • Year and Date: 2006-05-24
• [Presentation] ようこそSeifert surgeryの森へ (2006)
  • Author(s): K. Motegi
  • Organizer: トポロジーの展望
  • Place of Presentation: 九州大学西新プラザ 大会議室
  • Year and Date: 2006-03-17
• [Presentation] Networking Seifert fibered surgeries on knots (2006)
  • Author(s): 茂手木公彦
  • 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: 2006-02-21
• [Presentation] All integral slopes can be Seifert fibered slopes for hyperbolic knots (2005)
  • Author(s): 茂手木公彦
  • Organizer: 東北結び目セミナー
  • Place of Presentation: 国際蔵王高原ホテル
  • Year and Date: 2005-10-14
• [Presentation] On Seifert fibered slopes for hyperbolic knots (2005)
  • Author(s): K. Motegi
  • Organizer: First Arkansas-Oklahoma workshop in Topology and Geometry
  • Place of Presentation: University of Arkansas
  • Year and Date: 2005-05-20