Towards a classification theory of contact 3 -manifoldsand transverse knots

• Project/Area Number: 18740033
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Geometry
• Research Institution: University of Occupational and Environmental Health, Japan (2008); Naruto University of Education (2006-2007)
• Principal Investigator: TORISU Ichiro University of Occupational and Environmental Health, Japan, 医学部, 准教授 (50323134)
• 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 / モンテシノス絡み目 / 横断的絡み目 / 接触構造 / 有限型不変量 / ファイバー絡み目 / 2橋結び目 / モンテシノス結び目 / 横断的結び目 / 強自明性 / フロント射影図 / ルジャンドル結び目 / 2-adjacency relation

Research Abstract

結び目や絡み目をダイアグラムで表したときに、交差の入れ替えを複数箇所で同時に行ったときの結び目や絡み目の変化の解明について成果を得た。特に、2橋結び目とモンテシノス結び目の有限型不変量の研究について著しい成果を得ている。これは接触構造、有限型不変量や写像類群への応用が期待できるものである。特に、同じ有限型不変量を持つ異なる3次元多様体の具体的な構成や向き付け可能な閉曲面の写像類群の元の交換子長さの計算については直接的な応用がある。

Research Products

• [Journal Article] On 2-adjacency relation of two-bridge knots and links (2008)
  • Author(s): I. Torisu
  • Journal Title: Journal of Australian Mathematical Society vol. 84 Pages: 139-144
  • Peer Reviewed
• [Journal Article] On strongly 1-trivial Montesinos knot (2008)
  • Author(s): I. Torisu
  • Journal Title: Hiroshima Mathematical Journal vol. 38 Pages: 225-229
  • Peer Reviewed
• [Journal Article] On strongly 1-trivial Montesinos knot (2008)
  • Author(s): I. Torisu
  • Journal Title: Hiroshima Mathematical Journal 38 Pages: 225-229
  • Peer Reviewed
• [Journal Article] On 2-adjacency relation of links (2007)
  • Author(s): I. Torisu
  • Journal Title: the Proceedings of the International Workshop on Knot Theory for Scientific Objects Pages: 277-284
  • Peer Reviewed
• [Journal Article] On 2-adjacency relation of links (2007)
  • Author(s): I. Torisu
  • Journal Title: the Proceedings of the International Workshop on Knot Theory for Scientific Objects 2007 1 Pages: 277-284
  • Peer Reviewed
• [Journal Article] On 2-adjacency relation of two-bridge knots and links (2007)
  • Author(s): I.Torisu
  • Journal Title: Journal of the Australian Mathematical Society (To appear)