• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

RESEARCH OF TOPOLOGY RELATED THE MORSE THEORY AND RESEARCH OF COMPUTER ALGRBRA SYSTEM

Research Project

Project/Area Number 19540068
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionThe University of Electro-Communications

Principal Investigator

YAMAGUCHI Kohhei  The University of Electro-Communications, 電気通信学部, 教授 (00175655)

Co-Investigator(Kenkyū-buntansha) NAITO Toshiki  電気通信大学, 電気通信学部, 教授 (60004446)
KIDA Masanari  電気通信大学, 電気通信学部, 教授 (20272057)
OHNO Masahiro  電気通信大学, 電気通信学部, 准教授 (70277820)
YAMADA Yuichi  電気通信大学, 電気通信学部, 准教授 (30303019)
ISHIDA Haruhisa  電気通信大学, 電気通信学部, 准教授 (80312792)
Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2007: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywords位相幾何学 / モース理論 / 代数幾何学 / ホモトピー型 / 実代数幾何学 / 数式処理 / 実代数的多様体 / グースマン多様体 / GromovのH-原理 / 連続写像 / 代数的写像 / 同変ホモトピー型 / レンズ空間 / 実射影空間 / 有理ボローダウン / ホモロジー4球面 / レンズ空間手術 / 特異点 / derived category / 複素多様体 / 代数的多様体 / 正則写像 / 写像空間 / 4次元多様体 / 手術
Research Abstract

一般に、写像空間は無限次元位相空間であり、その空間の位相的性質を研究するのは難しい。本研究では、無限次元モース理論の原理を利用して、特に空間X,Yが実代数的多様体(実数係数の多変数多項式の零点集合で表現される特異点のない空間)の間の写像空間のホモトピー型を研究した。とくに、空間Yがグラスマン多様体で、空間Xが、その上のベクトル束がある条件を満足するとき、写像空間Map(X,Y)をその間の代数的写像のなす部分空間Alg(X,Y)でホモトピー的に近似できるという結果を証明できた。このことにより、Gromovのホモトピー原理が成り立つことを証明できた。さらに、空間X,Yが実射影空間の場合にその有限次元近似の次元を多項式の次数と関連した公式で表すこと(Atiyah-Jones型定理)にも成功した。

Report

(4 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (69 results)

All 2010 2009 2008 2007 Other

All Journal Article (34 results) (of which Peer Reviewed: 30 results) Presentation (29 results) Remarks (6 results)

  • [Journal Article] On positive linear Voltera-Stieltjes diffrential systems2009

    • Author(s)
      P.H. Anh Ngoc, S. Murakami, T. Naito, J. Son Shin, Y. Nagabuchi
    • Journal Title

      Integral Equations Operator Theorey vol.64

      Pages: 325-335

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Stability and robust stability of positive linear Voltera difference equations2009

    • Author(s)
      P.H. Anh Ngoc, T. Naito, J. Son Shin, s. Murakami
    • Journal Title

      Internat. J. Robust Nonlinear Control vol.19

      Pages: 552-568

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Quintic polynomials of Hashimoto-Tsunogai Brumer and Kummer2009

    • Author(s)
      M. Kida, G. Renault, K. Yokoyama
    • Journal Title

      Int. J. Number Theory vol.5

      Pages: 555-571

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Levi conditions to the Gevrey well-posedness for hyperbolic operators of higher order2009

    • Author(s)
      H. Ishida
    • Journal Title

      J. Math. Kyoto Univ. vol.49

      Pages: 173-191

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Oscilliatory properties for semilinear degenerate hyperbolic equations of second order2009

    • Author(s)
      H. Ishida, Y. Yuzawa
    • Journal Title

      J. Math. Anal. Appl. vol.356

      Pages: 624-632

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] A note on essential tori in the exterior of torus knots with twists2009

    • Author(s)
      M. Morimoto, Y. Yamada
    • Journal Title

      Kobe Math. J. vol.26

      Pages: 29-34

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Lens space surgeries as A'Campo's divide knots2009

    • Author(s)
      Y. Yamada
    • Journal Title

      Algebr. Geom. Topol. vol.9

      Pages: 397-428

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Spaces of maps from the closed Riemann surface into the 2-sphere2009

    • Author(s)
      K. Yamaguchi
    • Journal Title

      京都大学数理解析研究所講究録 vol.1670

      Pages: 77-83

    • Related Report
      2009 Final Research Report
  • [Journal Article] Lens space surgeries as A'Campo's divide knots2009

    • Author(s)
      Y.Yamada
    • Journal Title

      Algebr.Geom.Topol. 9

      Pages: 397-428

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Levi conditions to the Gevrey well-posedness for hyperbolic operators of Higher order2009

    • Author(s)
      H.Ishida
    • Journal Title

      J.Math.Kyoto Univ. 49

      Pages: 173-191

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Simplicial resolutions and their applications2008

    • Author(s)
      K. Yamaguchi
    • Journal Title

      京都大学数理解析研究所講究録 vol.1612

      Pages: 170-180

    • Related Report
      2009 Final Research Report
  • [Journal Article] Lyapunov exponents of solutions to linear differential equations with periodic forcing functions2008

    • Author(s)
      T. Naito, P. Huu Anh Ngoc, J. Son Shin
    • Journal Title

      J. Math. Annal. Appl. vol.342

      Pages: 349-353

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Representations and asymptic behavior of solutions to periodic linear difference equations2008

    • Author(s)
      T. Naito, P. Huu Anh Ngoc, J. Son Shin
    • Journal Title

      Funkcial Ekvac. vol.51

      Pages: 55-80

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Floquet representations and asymptic behavior of solutions to periodic linear difference equations2008

    • Author(s)
      T. Naito, P. Huu Anh Ngoc, J. Son Shin
    • Journal Title

      Hiroshima Math. J. vol.38

      Pages: 135-154

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] On stability and robust stability of positive linear Voltera equations2008

    • Author(s)
      P. Huu Anh Ngoc, T. Naito, J. Son Shin, S. Murakami
    • Journal Title

      J. Control Optim. vol.47

      Pages: 975-996

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Simplicial resolutions and their applications2008

    • Author(s)
      K. Yamaguchi
    • Journal Title

      数理解析研究所講究録 1612

      Pages: 170-180

    • Related Report
      2008 Annual Research Report
  • [Journal Article] Lyapunov exponents of solutions to linear differential Equations with periodic forcing functions2008

    • Author(s)
      T. Naito, P. H. A. Ngoc, J. Son
    • Journal Title

      J. Math. Anal. Appl. 342

      Pages: 349-353

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Representations and asymptotic behavior of solutions to periodic linear difference equations2008

    • Author(s)
      T. Naito, P. H. A. Ngoc, J. Son
    • Journal Title

      Funccial. Evvac. 51

      Pages: 55-80

    • NAID

      130000140700

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Resultants and universal coverings2007

    • Author(s)
      K. Yamaguchi
    • Journal Title

      J. Math. Kyoto Univ. vol.47

      Pages: 859-873

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] The homotopy approximation of spaces of algebraic maps between algebraic varieties2007

    • Author(s)
      K. Yamaguchi
    • Journal Title

      京都大学数理解析研究所講究録 vol.1569

      Pages: 123-131

    • Related Report
      2009 Final Research Report
  • [Journal Article] A deformation of the Alexander polynomials of knots yielding lens soaces2007

    • Author(s)
      T. Kadokami, Y. Yamada
    • Journal Title

      Bull. Austral. Math. Soc. vol.75

      Pages: 75-89

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] On stability of a class of positive linear functional difference equations2007

    • Author(s)
      P. Huu Anh Ngoc, T. Naito, J. Son Shin
    • Journal Title

      Math. Control Signals Systems vol.19

      Pages: 361-382

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Characterizations of linear Voltera integral equations with negative kernels2007

    • Author(s)
      T. Naito, J. Son Shin, S. Murakami, P. Huu Anh Ngoc
    • Journal Title

      J. Math. Anal. Appl. vol.335

      Pages: 298-313

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Characterization of positive linear functional differential equations2007

    • Author(s)
      P. Huu Anh Ngoc, T. Naito, J. Son Shin
    • Journal Title

      Funkcial Ekvac. vol.50

      Pages: 1-17

    • NAID

      130000140678

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Characerization of positive linear Voltera integro-differrential systems2007

    • Author(s)
      T. Naito, S. Murakami, J. Son Shin, P. Huu Anh Ngoc
    • Journal Title

      Integral Equations Operator Theory vol.58

      Pages: 255-272

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Stability radii of positive linear functional differential systems in Banach spaces2007

    • Author(s)
      P. Huu Anh Ngoc, N.V. Minh, T. Naito
    • Journal Title

      Int. J. Evol. Equ. vol.2

      Pages: 75-7

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Stability radii of higher order linear difference systems under multipertubations2007

    • Author(s)
      P. Huu Anh Ngoc, Thai Bao Tran, T. Naito
    • Journal Title

      J. Differentail Equ. Appl. vol.13

      Pages: 15-24

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Stability radius of linear parametervarying systems and applications2007

    • Author(s)
      P. Huu Anh Ngoc, T. Naito
    • Journal Title

      J. Math. Anal. Appl. vol.328

      Pages: 170-191

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Resultants and universal coverings2007

    • Author(s)
      Kohhei Yamaguchi
    • Journal Title

      J. Math. Kyoto Univ. 47-4(印刷中)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Erratum to"The homotopy of spaces of maps between real projective spaces"2007

    • Author(s)
      Kohhei Yamaguchi
    • Journal Title

      J. Math. Soc. Japan 59-4

      Pages: 1235-1237

    • NAID

      10019989468

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On stability of a class of positive linear functional differential equations2007

    • Author(s)
      P. H. H. A. Ngoc, T. Nato and J. Song
    • Journal Title

      Math. Control Signals Systems 19-4

      Pages: 361-382

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Spaces of algebraic maps from real projective spaces into complex projective spaces

    • Author(s)
      A. Kozlowski, K. Yamaguchi
    • Journal Title

      Contemporary Math. (to appear)

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Spaces of algebraic and continuous maps between real algebraic varieties

    • Author(s)
      M. Adamaszek, A. Kozlowski, K. Yamaguch
    • Journal Title

      Quart. J. Math. (to appear)

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Spaces of algebraic maps from real projective spaces into complex Projective spaces

    • Author(s)
      A.Kozlowski, K.Yamaguchi
    • Journal Title

      Contemporary Math.(to appear)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Presentation] Lens space surgeries along certain 2-components links and Reidemeister-Turaev torsion2010

    • Author(s)
      門上晃久, 山田裕一
    • Organizer
      日本数学会年会トポロジー分科会講演アブストラクト
    • Place of Presentation
      慶応大学日吉キャンパス
    • Year and Date
      2010-03-26
    • Related Report
      2009 Final Research Report
  • [Presentation] The homotopy type of spaces of algebraic maps I2010

    • Author(s)
      M. Adamaszek, A. Kozlowski, K. Yamaguchi
    • Organizer
      日本数学会年会トポロジー分科会講演アブストラクト
    • Place of Presentation
      慶応大学日吉キャンパス
    • Year and Date
      2010-03-25
    • Related Report
      2009 Final Research Report
  • [Presentation] The homotopy type of spaces of Algebraic maps II2010

    • Author(s)
      M. Adamaszek, A. Kozlowski, K. Yamaguchi
    • Organizer
      日本数学会年会トポロジー分科会講演アブストラクト
    • Place of Presentation
      慶応大学日吉キャンパス
    • Year and Date
      2010-03-25
    • Related Report
      2009 Final Research Report
  • [Presentation] Every Berge's knot of lens space surgery is a divide knot2010

    • Author(s)
      山田裕一
    • Organizer
      The sixth East Asian School of Knots and related topics
    • Place of Presentation
      天津(中国)
    • Year and Date
      2010-01-28
    • Related Report
      2009 Final Research Report
  • [Presentation] 退化双曲型方程式に対する振動定理について2010

    • Author(s)
      石田晴久
    • Organizer
      第25回松山キャンプ
    • Place of Presentation
      愛媛県総合社会福祉会館
    • Year and Date
      2010-01-06
    • Related Report
      2009 Final Research Report
  • [Presentation] 退化双曲型方程式の振動定理と非振動解について2009

    • Author(s)
      石田晴久
    • Organizer
      第16回超局所解析と古典解析
    • Place of Presentation
      休暇村竹野会館
    • Year and Date
      2009-11-02
    • Related Report
      2009 Final Research Report
  • [Presentation] フリードマン原論文に学ぶ6章2009

    • Author(s)
      山田裕一
    • Organizer
      8章, キャッソン・フリードマン理論研究会
    • Place of Presentation
      けいはんなプラザホテル
    • Year and Date
      2009-10-19
    • Related Report
      2009 Final Research Report
  • [Presentation] 退化双曲型方程式の振動問題について2009

    • Author(s)
      石田晴久
    • Organizer
      八王子偏微分方程式研究集会
    • Place of Presentation
      八王子セミナーハウス
    • Year and Date
      2009-10-11
    • Related Report
      2009 Final Research Report
  • [Presentation] 4次元多様体を表すKirby Diagram2009

    • Author(s)
      山田裕一
    • Organizer
      基礎から応用
    • Place of Presentation
      筑波大学
    • Year and Date
      2009-10-01
    • Related Report
      2009 Final Research Report
  • [Presentation] 退化双曲型方程式の振動問題について2009

    • Author(s)
      石田晴久
    • Organizer
      日本数学会2009年度秋季総合会函数方程式論分科会講演アブストラクト
    • Place of Presentation
      大阪大学理学部
    • Year and Date
      2009-09-24
    • Related Report
      2009 Final Research Report
  • [Presentation] The space of curves on the 2-sphere2009

    • Author(s)
      山口耕平
    • Organizer
      研究集会「変換群の新たな展開」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2009-08-19
    • Related Report
      2009 Final Research Report
  • [Presentation] The space of curves on the 2-sphere2009

    • Author(s)
      山口耕平
    • Organizer
      京都大学数理解析研究所短期共同研究「変換群の新たな展開」研究集会
    • Place of Presentation
      京都大学数理解析研究所(京都市)
    • Year and Date
      2009-08-19
    • Related Report
      2009 Annual Research Report
  • [Presentation] Asymptotics for linear differential systems with variable coefficients via new characteristic numbers2009

    • Author(s)
      石田晴久
    • Organizer
      第24回松山キャンプ
    • Place of Presentation
      山口大学理学部
    • Year and Date
      2009-03-15
    • Related Report
      2009 Final Research Report
  • [Presentation] Dehn surgery along A'Campo's divide knots, Lens spaces and plane curves, Branched Coverings2009

    • Author(s)
      山田裕一
    • Organizer
      Degenerations, and Related Topics
    • Place of Presentation
      広島大学
    • Year and Date
      2009-03-09
    • Related Report
      2009 Final Research Report
  • [Presentation] 新しい特性数による変数係数線形微分方程式系の解の挙動について2009

    • Author(s)
      石田晴久
    • Organizer
      日本大学理工学部偏微分方程式研究集会
    • Place of Presentation
      日本大学理工学部
    • Year and Date
      2009-03-04
    • Related Report
      2009 Final Research Report
  • [Presentation] Lens space surgery along A'Campo's divide knots II2009

    • Author(s)
      Y. Yamada
    • Organizer
      The 5th East Asian School of Knots and Related Topics
    • Place of Presentation
      慶州(韓国)
    • Year and Date
      2009-01-12
    • Related Report
      2009 Final Research Report
  • [Presentation] 特性数による変数係数線形常微分方程式系の解の漸近挙動について2008

    • Author(s)
      石田晴久
    • Organizer
      第15回超局所解析と古典解析
    • Place of Presentation
      横浜港のホテル
    • Year and Date
      2008-11-09
    • Related Report
      2009 Final Research Report
  • [Presentation] 多項式位数の解をもつ線形常微分方程式系の性質について2008

    • Author(s)
      石田晴久
    • Organizer
      米子偏微分方程式研究集会
    • Place of Presentation
      米子工業高等専門学校
    • Year and Date
      2008-10-12
    • Related Report
      2009 Final Research Report
  • [Presentation] Generalized rational blow-down, torus knots, and Euclidean Algorithm2008

    • Author(s)
      山田裕一
    • Organizer
      日本数学会秋季総合分科会講演アブストラクト
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-25
    • Related Report
      2009 Final Research Report
  • [Presentation] Simplicial resolutions and their applications2008

    • Author(s)
      山口 耕平
    • Organizer
      数理解析研究所短期共同研究集会「変換群の研究とその周辺」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2008-05-22
    • Related Report
      2008 Annual Research Report
  • [Presentation] Levi conditions for higher order hyperbolic equations by weight functions2008

    • Author(s)
      石田晴久
    • Organizer
      日本数学会2008年度年会函数方程式論分科会講演アブストラクト
    • Place of Presentation
      近畿大学理工学部
    • Year and Date
      2008-03-23
    • Related Report
      2009 Final Research Report
  • [Presentation] Torus knots, Generalized rational blow-down, and lens space surgery of Type 7, 82008

    • Author(s)
      山田裕一
    • Organizer
      研究集会「4次元トポロジー」
    • Place of Presentation
      広島大学
    • Year and Date
      2008-02-08
    • Related Report
      2009 Final Research Report
  • [Presentation] Colombini-Taglialatela型のLevi条件の改良への試み2008

    • Author(s)
      石田晴久
    • Organizer
      第23回松山キャンプ
    • Place of Presentation
      山口大学理学部
    • Year and Date
      2008-01-06
    • Related Report
      2009 Final Research Report
  • [Presentation] Oscillatory properties for semilinear degenerate hyperbolic equations I2007

    • Author(s)
      石田晴久
    • Organizer
      山中湖偏微分方程式シンポジウム
    • Place of Presentation
      東海大学山中湖セミナーハウス
    • Year and Date
      2007-10-08
    • Related Report
      2009 Final Research Report
  • [Presentation] Generalized rational blow-down and Euclidean Algorithm2007

    • Author(s)
      山田裕一
    • Organizer
      研究集会「低次元幾何学と無限次元幾何学」
    • Place of Presentation
      東京大学玉原国際セミナーハウス
    • Year and Date
      2007-09-13
    • Related Report
      2009 Final Research Report
  • [Presentation] Kirby Calc.入門2007

    • Author(s)
      山田裕一
    • Organizer
      研究集会「低次元幾何学と無限次元幾何学」
    • Place of Presentation
      東京大学玉原国際セミナーハウス
    • Year and Date
      2007-09-12
    • Related Report
      2009 Final Research Report
  • [Presentation] Oscillatory properties for semilinear degenerate hyperbolic equations2007

    • Author(s)
      石田晴久
    • Organizer
      2007年夏の偏微分方程式シンポジウム
    • Place of Presentation
      ホテル箱根パウエル
    • Year and Date
      2007-08-28
    • Related Report
      2009 Final Research Report
  • [Presentation] The homotopy of spaces of algebraic maps and related topics2007

    • Author(s)
      山口 耕平
    • Organizer
      研究集会「変換群の理論とその応用」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2007-05-31
    • Related Report
      2007 Annual Research Report
  • [Presentation] 多様体の中で具体的にキャッソンハンドルを"作る"(Z. BizacaとR. Gompfの結果紹介)2007

    • Author(s)
      山田裕一
    • Organizer
      キャッソンハンドル勉強会
    • Place of Presentation
      東京大学玉原国際セミナーハウス
    • Year and Date
      2007-05-27
    • Related Report
      2009 Final Research Report
  • [Remarks]

    • URL

      http://kjk.office.uec.ac.jp/Profiles/0001/0000339/profile.html

    • Related Report
      2009 Final Research Report
  • [Remarks]

    • URL

      http://xxx.yukawa.kyoto-u.ac.jp/PS_cache/arxiv/pdf/0812/0812.3954v2.pdf

    • Related Report
      2009 Final Research Report
  • [Remarks]

    • URL

      http://xxx.yukawa.kyoto-u.ac.jp/PS_cache/arxiv/pdf/0809/0809.4893v3.pdf

    • Related Report
      2009 Final Research Report
  • [Remarks]

    • URL

      http://kjk.office.uec.ac.jp/Profiles/0001/0000339/profile.html

    • Related Report
      2009 Annual Research Report
  • [Remarks]

    • URL

      http://kjk.office.uec.ac.jp/Profiles/OOO1/0000339/thesesl.html

    • Related Report
      2008 Annual Research Report
  • [Remarks]

    • URL

      http://kjk.office.uec.ac.jp/Profiles/0001/0000339/theses1.html

    • Related Report
      2007 Annual Research Report

URL: 

Published: 2007-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi