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2013 Fiscal Year Final Research Report

Relations of formal power series of one variable and coding of space curves by iterated path integrals

Research Project

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Project/Area Number 23540236
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Global analysis
Research InstitutionOchanomizu University

Principal Investigator

NAKAI Isao  お茶の水女子大学, 大学院人間文化創成科学研究科, 教授 (90207704)

Project Period (FY) 2011 – 2013
Keywords力学系 / 関係式 / センター問題 / WEB幾何学
Research Abstract

The words consisting of two letters X,Y and their inverses constitute a group structure in algebra, where the concatenation of words is the product. An element of this group defines a polygonal path with vertices on the integral lattice. Plane curves are regarded as generalization of such linear paths, hence words of X,Y. From this point of view, the group of plane curves are investigated, especially curves are presented as generalized words of X,Y and the logarithms of those curves are investigated as elements of the free algebra generated by X,Y, and some results are obtained.

  • Research Products

    (4 results)

All 2014 2012 2011

All Journal Article (1 results) (of which Peer Reviewed: 1 results) Presentation (3 results)

  • [Journal Article] Webs and Singularities2014

    • Author(s)
      NAKAI, Isao
    • Journal Title

      Journal of Singularities

      Volume: Vol 9(掲載ページ未定)

    • Peer Reviewed
  • [Presentation] Geometry of Path group Feuilletages et equations differentielles complexes2012

    • Author(s)
      NAKAI, Isao
    • Organizer
      国際議
    • Place of Presentation
      フランス, マルセイユ CIRM 研究所
    • Year and Date
      2012-10-16
  • [Presentation] Webs and Singularities Les Jornees textiles2011

    • Author(s)
      NAKAI, Isao
    • Organizer
      国際会議
    • Place of Presentation
      Universite de Rennes 1, フランス, レンヌ
    • Year and Date
      2011-11-23
  • [Presentation] Webs and Singularities Resolution of singularities and related topics2011

    • Author(s)
      NAKAI, Isao
    • Organizer
      国際会議
    • Place of Presentation
      Tordesillas, スペイン
    • Year and Date
      2011-09-22

URL: 

Published: 2015-07-16  

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