A study of spatial graphs from topological viewpoint

• Project/Area Number: 24540100
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Waseda University
• Principal Investigator: TANIYAMA KOUKI 早稲田大学, 教育・総合科学学術院, 教授 (10247207)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000); Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2013: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000); Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 位相幾何学 / 結び目理論 / 空間グラフ / 結び目

Outline of Final Research Achievements

We have studied puzzle ring problem by formulating it into a problem of site-specific crossing change distance of spatial graphs. In stead of group presentation arguments known so far we have used covering space arguments. We have also studied when a composition of discontinuous maps is continuous.

Research Products

• [Journal Article] Strong and weak $(1,3)$ homotopies on knot projections (2015)
  • Author(s): N. Ito, Y. Takimura and K. Taniyama
  • Journal Title: Osaka Journal of Mathematics Volume: to appear
  • NAID: 120005986343
  • Peer Reviewed
• [Journal Article] Discontinuous maps whose iterations are continuous (2014)
  • Author(s): K. Taniyama
  • Journal Title: Nihonkai Mathematical Journal Volume: 25 Pages: 119-125
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Mapping a knot by a continuous map (2014)
  • Author(s): K. Taniyama
  • Journal Title: J. Knot Theory Ramifications Volume: 23 Issue: 10 Pages: 1450052-1450052
  • DOI: 10.1142/s0218216514500527
  • Peer Reviewed
• [Journal Article] Plane curves in an immersed graph in R^2. (2013)
  • Author(s): M. Sakamoto and K. Taniyama
  • Journal Title: J. Knot Theory Ramifications Volume: 22 Issue: 02 Pages: 1-10
  • DOI: 10.1142/s021821651350003x
  • Peer Reviewed
• [Journal Article] $\triangle Y$-exchanges and the Conway-Gordon theorems (2012)
  • Author(s): Ryo Nikkuni, Kouki Taniyama
  • Journal Title: Journal of Knot Theory and its Ramifications Volume: 7 Issue: 07 Pages: 1-14
  • DOI: 10.1142/s0218216512500678
  • Peer Reviewed
• [Journal Article] Multiplicity of a space over another space (2012)
  • Author(s): K. Taniyama
  • Journal Title: Journal of the Mathematical Society of Japan Volume: 64 Issue: 3 Pages: 823-849
  • DOI: 10.2969/jmsj/06430823
  • NAID: 10031177251
  • ISSN: 0025-5645, 1881-1167, 1881-2333
  • Peer Reviewed
• [Presentation] Site-specifc Gordian distances of spatial graphs (2015)
  • Author(s): K. Taniyama
  • Organizer: Conference on Knot Theory and Its Applications to Physics and Quantum Computing
  • Place of Presentation: The University of Texas at Dallas
  • Year and Date: 2015-01-07
• [Presentation] Discontinuous maps whose iterations are continuous (2014)
  • Author(s): 谷山公規
  • Organizer: 第87回米沢数学セミナー
  • Place of Presentation: 山形大学工学部
  • Year and Date: 2014-06-18
• [Presentation] Plane curves in an immersed graph in ${\mathbb R}^3$
  • Author(s): Kouki Taniyama
  • Organizer: International Workshop on Spatial Graphs 2013
  • Place of Presentation: Tokyo Woman’s Christian University