Study of spatial graphs from the topological viewpoint

• Project/Area Number: 18540101
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: Waseda University
• Principal Investigator: TANIYAMA Kouki Waseda University, 教育・総合科学学術院, 教授 (10247207)
• Project Period (FY): 2006 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥4,060,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥660,000); Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2007: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2006: ¥1,200,000 (Direct Cost: ¥1,200,000)
• Keywords: 結び目 / 空間グラフ

Research Abstract

非自明な結び目を一つ固定したとき、その射影図の結び目解消数はいくらでも大きく出来ることを示した。また、円周からある集合への写像で、その多重点が高々有限個の2重点のみであるものについて、円周をある2つの単純弧に分解してそれぞれの単純弧への制限写像が単射になるようにすることが出来るかどうかを、その写像から定まるコード図式の言葉で決定した。またほとんどの交点が正交点であるような射影図を持つ絡み目の符号数などについて研究した。

Research Products

• [Journal Article] An irreducible rectangle tiling contains a spiral, Journal of Geometry (2008)
  • Author(s): T. Motohashi and K. Taniyama,
  • Journal Title: 90 Pages: 175-184
  • Peer Reviewed
• [Journal Article] An irreducible rectangle tiling contains a spiral (2008)
  • Author(s): Tomoe Motohashi, Kouki Taniyama
  • Journal Title: Journal of Geometry 90 Pages: 175-184
  • Peer Reviewed
• [Journal Article] 2-irreducibility of spatial graphs (2006)
  • Author(s): F.Lei, K.Taniyama, G.Zhang
  • Journal Title: Journal of Knot Theory and its Ramifications 15 Pages: 31-41
• [Journal Article] Unknotting numbers of diagrams of a given nontrivial knot are unbounded, to appear in J. Knot Theory and Ramifications
  • Author(s): K. Taniyama
  • Journal Title: [掲載確定] Pages: 0-0
  • Peer Reviewed
• [Journal Article] An irreducible rectangle tiling contains a spiral
  • Author(s): Tomoe Motohashi and Kouki Taniyama
  • Journal Title: Journal of Geometry (to appear)
  • Peer Reviewed
• [Presentation] Circle immersions that can be divided into two arc embeddings (2009)
  • Author(s): K. Taniyama
  • Organizer: KNOTS IN WASHINGTON XXVIII
  • Place of Presentation: George Washington University, Washington DC, USA.
  • Year and Date: 2009-02-28
• [Presentation] Unknotting numbers of diagrams of a given nontrivial knot are unbounded (2008)
  • Author(s): K. Taniyama
  • Organizer: KNOTS IN WASHINGTON XXVI
  • Place of Presentation: George Washington University, Washington DC, USA.
  • Year and Date: 2008-04-20