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Research for low-dimensional manifdds with various geometric structures

Research Project

Project/Area Number 10640074
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

VE Masaaki  Kyoto Univ., Integrated Human Studies, Ass. Professor, 総合人間学部, 助教授 (80134443)

Co-Investigator(Kenkyū-buntansha) NISHIWADA Kimimasa  Kyoto Univ., Integrated Human Studies, Professor, 総合人間学部, 教授 (60093291)
KATO Shinichi  Kyoto Univ., Integrated Human Studies, Ass. Professor, 総合人間学部, 助教授 (90114438)
IMANISHI Hideki  Kyoto Univ., Integrated Human Studies, Professor, 総合人間学部, 教授 (90025411)
VSHIKI Shigehiro  Kyoto Univ., Graduate School of Human and Environmental Studies Professor, 総合人間学部, 教授 (10093197)
MORIMOTO Yoshinori  Kyoto Univ., Integrated Human Studies, Professor, 総合人間学部, 教授 (30115646)
日置 尋久  京都大学, 総合人間学部, 助手 (70293842)
Project Period (FY) 1998 – 1999
Project Status Completed (Fiscal Year 1999)
Budget Amount *help
¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 1999: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 1998: ¥1,400,000 (Direct Cost: ¥1,400,000)
Keywordshomology 3-sphere / Seifert manifolcl / cobordism / foliation / complex dynamical system / Ruelle operator / smoothing effect / hypoellipticity / 4次元多様体 / Seiberg-Witten理論 / 球等質空間 / 双曲型偏微分方程式 / ヘッケ作用素 / 3次元シーン計測法
Research Abstract

As part of the study of 3 and 4-manifolds, Ue showed the reciprocity for the values of W invariants of homology 3-spheres. As its application, he showed that the W invariant of Seifert homology 3-sphere coincides with its Neumann-Siebenmann invariant, and when number of singular fibers is at most six, this invariant is a homology cobordism invariant. Imanishi studied the homeomorphism groups of foliated manifolds. He showed that any group of homeomorphisms preserving leaves is perfect, and that the homeomorphism groups preserving the codimension 1 foliations are sometimes perfect, while they are not perfect when the manifolds have dense leaves with trivial holonomy. Ushiki studied the Ruelle operators associated with 1-dimensional complex dynamical systems. He showed that dynamical zeta-functions appear as the factors of the Fredholm determinants, and the conditions on the convergence radii and the zeroes of the remaining factors are given by the informations on the singularities of th … More e iterations of the dynamical systems, and also they are described by the infomations on the singularities of the iterations of the dynamical systems, and also they are described by the information of forward orbits of the singularities. Morimoto studied the initial value problems on Schrodinger equations. He showed that some micro-local analytic smoothing effects appear if the initial data have some estimates of Gevrey order 2. He also gave the characterization of hypoellipticity of second order infinitely degenerate elliptic operators using Wick calculus, and the hypoellipticity of some class of first order pseudo differential operators of Egorov type. Kato gave the general formula for spherical functions on symmetric spaces and the explicit algorithm of its computation. Nishiwada studied the property of the moments concerning the second order hyperbolic partial differential equations, Yamauchi studied the eigenvalues of the Hecke operators on the space of automorphic functions, and Asano studied the nonlinear phenomena. Less

Report

(3 results)
  • 1999 Annual Research Report   Final Research Report Summary
  • 1998 Annual Research Report

Research Products

(21 results)

All Other

All Publications (21 results)

  • [Publications] 上 正明: "W-invariants and Neumann-Siebenmann invariants for seifert homology 3-spheres"(未定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 加藤信一: "Whittaker-Shintani Functions for Orthogonal Groups"(未定). (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 今西英器: "On commutators of foliation preserving homemorphisms"J.Math.Soc.Japan.. 51巻. 227-236 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 森本芳則: "Hypoellipticity for operators of infinitely degenerate Egorov type"Tsukuba J.Math.. 23巻2号. 215-224 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 森本芳則: "Remark on the analytic smoothing for the schrodinger equation"Indiana Univ.Math.J.. (未定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 宇敷重広: "Complex Ruelle Operator in a Parabolic Basin,Research on Complex Dynamical Systems-where it is and where it is going-"RIMS Kokyuroku. 1087巻. 108-119 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Masaaki Ue: "W-invariants and Neumann-Siebenmann invariants for seifert homology 3-spheres."(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Shinichi Kato: "Whittaker-Shintani Functions for Orthogonal Groups"(to appear). (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Hideki Imanishi: "On Commutators of foliation preserring homemorphisms"J. Math. Soc. Japan. Vol.51. 227-236 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Yoshinori Morimoto: "Hypoellipticity for operators of infinitely degenerate Egorov Type"Tsukuba J. Math. Vol.23 NO.2. 215-224 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Yoshinori Morimoto: "Remark on the analytic Smoothing for the Schrodinger equation"Indiana Univ. Math. J.. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Shigehiro Ushiki: "Complex Ruelle Operator in a Parabolic Basin, Research on Complex Pynamical Systems-where it is and where it is going-."RIMS Kokyuroku. No.1087. 108-119 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 上 正明: "W-invariants and Neumann-Siebenmann invariants for Seifert homology3-spheres"未定. (未定).

    • Related Report
      1999 Annual Research Report
  • [Publications] 加藤 信一: "Whittaker-Shintani Functions for Orthogonal Groups"未定. (未定). (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] 今西 英器: "On Commutators of foliation preserving homemorphisms"J.Math.Soc.Japan. 51巻. 227-236 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 森本 芳則: "Hypoellipticity for operators of infinitely degenerate Egorov type"Tsukuba J.Math.. 23巻2号. 215-224 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 森本 芳則: "Remark on the analytic smoothing for the Stronger equation"Indiana Univ.Math.J.. (未定).

    • Related Report
      1999 Annual Research Report
  • [Publications] 宇敷 重広: "Complex Ruelle Operator in a parabolic Basin, Research on Complex Dynamical Systems -where it is and where it is going-"RIMS Kokyuroku. 1087巻. 108-119 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Masaaki UE: "Exotic group actions in dimension four and Seiberg Witten theory" Proc.Japan.Acd.74・4. 68-70 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] S.Ushiki: "Complex Ruelle Operator and Hyperbolic Complex Dynamical Systems" RIMS Kokyuroku. 1072巻. 50-61 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] S.Ushiki: "Complex Ruelle Operator in a Parabolic Basin."

    • Related Report
      1998 Annual Research Report

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Published: 1998-03-31   Modified: 2016-04-21  

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