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A Classification of Minimal Charts

Research Project

Project/Area Number 20540093
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionTokai University

Principal Investigator

SHIMA Akiko  Tokai University, 理学部, 准教授 (50317765)

Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords位相幾何 / surface knot / chart / white vertex / surface braid
Research Abstract

A chart is an oriented labeled graph on a disk which represents a surface link, i.e. an embedded surface in the 4-dimensional space. This is a remarkable method. We research about a classification of charts with at most three crossings. The main result is as follows : Any minimal chart with at most three crossing is either a ribbon chart, or a disjoint union of a chart representing a 2-twist spun trefoil, hoops and free edges. That is, any minimal chart with at most three crossing is a chart representing a 2-twist spun trefoil modulo ribbon charts.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (19 results)

All 2011 2010 2009 Other

All Journal Article (14 results) (of which Peer Reviewed: 14 results) Presentation (5 results)

  • [Journal Article] There no exists minimal charts of type (2,2,2)2011

    • Author(s)
      Teruo Nagase, Nemoto Daisuke, Akiko Shima
    • Journal Title

      Proceedings of the School of Science 46

      Pages: 1-31

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] There no exists minimal charts of type (2,2,2)2011

    • Author(s)
      Teruo Nagase, Nemoto Daisuke, Akiko Shima
    • Journal Title

      Proceedings of the School of Science

      Volume: 46 Pages: 1-31

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Any chart with at most one crossing is a ribbon chart2010

    • Author(s)
      Teruo Nagase, Akiko Shima
    • Journal Title

      Topology and its Applications 157

      Pages: 1703-1720

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] On charts with two crossings I : There exist no NS-tangles in a minimal chart2010

    • Author(s)
      Teruo Nagase, Akiko Shima
    • Journal Title

      J.Math.Sci.Univ.Tokyo 17

      Pages: 217-241

    • NAID

      120006906054

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Properties of Minimal Charts and Their Applications III2010

    • Author(s)
      Teruo Nagase, Akiko Shima
    • Journal Title

      Tokyo Journal of Mathematics 13

      Pages: 373-392

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Any chart with at most one crossing is a ribbon chart2010

    • Author(s)
      Teruo Nagase, Akiko Shima
    • Journal Title

      Topology and its Applications

      Volume: 157 Pages: 1703-1720

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On charts with two crossings I : There exist no NS-tangles in a minimal chart2010

    • Author(s)
      Teruo Nagase, Akiko Shima
    • Journal Title

      J.Math.Sci.Univ.Tokyo

      Volume: 17 Pages: 217-241

    • NAID

      120006906054

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Properties of Minimal Charts and Their Applications III2010

    • Author(s)
      Teruo Nagase, Akiko Shima
    • Journal Title

      Tokyo Journal of Mathematics

      Volume: 13 Pages: 373-392

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Properties of minimal charts and their applications II2009

    • Author(s)
      Teruo Nagase, Akiko Shima
    • Journal Title

      Hiroshima Mathematical Journal 39

      Pages: 1-35

    • NAID

      110007014251

    • Related Report
      2010 Final Research Report 2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Minimal n-charts with four white vertices

    • Author(s)
      Satoru Ishida, Teruo Nagase, Akiko Shima
    • Journal Title

      Journal of Knot Theory and Its Ramifications (in press)

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Minimal n-charts with four white vertices

    • Author(s)
      Satoru Ishida, Teruo Nagase, Akiko Shima
    • Journal Title

      Journal of Knot Theory and Its Ramifications

      Volume: in press

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Properties of minimal charts and their applications III

    • Author(s)
      Teruo Nagase, Akiko Shima
    • Journal Title

      Tokyo Journal of Mathematics (in press)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Minimal n-charts with four white vertices

    • Author(s)
      Teruo Nagase, Akiko Shima
    • Journal Title

      Journal of Knot Theory and its Ramifications (in press)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Any chart with at most one crossing is a ribbon chart

    • Author(s)
      Teruo Nagase, Akiko Shima
    • Journal Title

      Topology and its applications (in press)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Presentation] Crossingを3つ含むchartについて2010

    • Author(s)
      Teruo Nagase, Akiko Shima
    • Organizer
      日本数学会2010年度年会
    • Place of Presentation
      慶應義塾大学
    • Year and Date
      2010-03-26
    • Related Report
      2010 Final Research Report 2009 Annual Research Report
  • [Presentation] On the crossings in minimal charts2010

    • Author(s)
      Teruo Nagase, Akiko Shima
    • Organizer
      International Conference on Analysis and Applications
    • Place of Presentation
      Sultan Qaboos University, Akiko Shima
    • Year and Date
      2010-01-25
    • Related Report
      2010 Final Research Report
  • [Presentation] On the crossings in minimal charts2010

    • Author(s)
      Teruo Nagase, Akiko Shima
    • Organizer
      International Conference on Analysis and Applications
    • Place of Presentation
      Sultan Qaboos University
    • Year and Date
      2010-01-25
    • Related Report
      2009 Annual Research Report
  • [Presentation] On charts with three crossings2009

    • Author(s)
      Teruo Nagase, Akiko Shima
    • Organizer
      4次元のトポロジー
    • Place of Presentation
      広島大学
    • Year and Date
      2009-01-28
    • Related Report
      2010 Final Research Report
  • [Presentation] On charts with three corssings2009

    • Author(s)
      Teruo Nagase, Akiko Shima
    • Organizer
      4次元のトポロジー
    • Place of Presentation
      広島大学
    • Year and Date
      2009-01-28
    • Related Report
      2008 Annual Research Report

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Published: 2008-04-01   Modified: 2016-04-21  

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