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A study of spatial graphs from topological viewpoint

Research Project

Project/Area Number 21540099
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionWaseda 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) 2009 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords位相幾何 / 結び目 / 空間グラフ
Research Abstract

We have studied spatial graphs from a viewpoint of the concept multiplicity. We have define the concept multiplicity on a category. As an example, we defined a multiplicity of a knot over another knot. For a continuous map from a three-dimensional Euclidean space to the three-dimensional Euclidean space that maps a knot to another knot, we studied their knot types.

Report

(4 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (12 results)

All 2011 2010 2009 Other

All Journal Article (12 results) (of which Peer Reviewed: 3 results)

  • [Journal Article] On intrinsically knotted or completely 3-linked graphs2011

    • Author(s)
      R. Hanaki, R. Nikkuni, K. Taniyama, and A. Yamazaki
    • Journal Title

      Pacific J. Math.

      Volume: Vol.252, No.2 Pages: 407-425

    • Related Report
      2011 Final Research Report
  • [Journal Article] On intrinsically knotted or completely 3-linked graphs2011

    • Author(s)
      R. Hanaki, R. Nikkuni, K. Taniyama, and A. Yamazaki
    • Journal Title

      Pacific J. Math.

      Volume: Vol.252 Issue: 2 Pages: 407-425

    • DOI

      10.2140/pjm.2011.252.407

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Braid presentation of spatial graphs2010

    • Author(s)
      K. Kanno and K. Taniyama
    • Journal Title

      Tokyo J. Math.

      Volume: 33no.2 Pages: 509-522

    • Related Report
      2011 Final Research Report
  • [Journal Article] Almost positive links have negative signature2010

    • Author(s)
      J. Przytycki and K. Taniyama
    • Journal Title

      Journal of Knot Theory and Its Ramifications

      Volume: Vol.19, No.2 Pages: 187-289

    • Related Report
      2011 Final Research Report
  • [Journal Article] A graph-theoretic approach to a partial order of knots and links2010

    • Author(s)
      T. Endo and T. Itoh and K. Taniyama
    • Journal Title

      Topology Appl.

      Volume: 157 Pages: 1002-1010

    • Related Report
      2011 Final Research Report
  • [Journal Article] Circle immersions that can be divided into two arc embeddings2010

    • Author(s)
      K. Taniyama
    • Journal Title

      Proc. Amer. Math. Soc.

      Volume: 138 Pages: 743-751

    • Related Report
      2011 Final Research Report
  • [Journal Article] Circle immersions that can be divided into two arc embeddings2010

    • Author(s)
      Kouki Taniyama
    • Journal Title

      Proc.Amer.Math.Soc.

      Volume: 138 Pages: 743-751

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Circle immersions that can be divided into two are embeddings2010

    • Author(s)
      Kouki Taniyama
    • Journal Title

      Proc.Amer.Math.Soc. 138

      Pages: 743-751

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Symmetries of spatial graphs and Simon invariants2009

    • Author(s)
      R. Nikkuni and K. Taniyama
    • Journal Title

      Fund. Math.

      Volume: 205 Pages: 219-236

    • Related Report
      2011 Final Research Report
  • [Journal Article] Unknotting numbers of diagrams of a given nontrivial knot are unbounded2009

    • Author(s)
      K. Taniyama
    • Journal Title

      Journal of Knot Theory and its Ramifications

      Volume: 18no.8 Pages: 1049-1063

    • Related Report
      2011 Final Research Report
  • [Journal Article] $\triangle Y$-exchanges and the Conway-Gordon theorems

    • Author(s)
      R. Nikkuni and K. Taniyama
    • Journal Title

      Journal of Knot Theory and Its Ramifications

    • Related Report
      2011 Final Research Report
  • [Journal Article] Multiplicity of a space over another space

    • Author(s)
      K. Taniyama
    • Journal Title

      Journal of the Mathematical Society of Japan

    • NAID

      10031177251

    • Related Report
      2011 Final Research Report

URL: 

Published: 2009-04-01   Modified: 2016-04-21  

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