Project/Area Number  10640074 
Research Category 
GrantinAid for Scientific Research (C).

Section  一般 
Research Field 
Geometry

Research Institution  KYOTO UNIVERSITY 
Principal Investigator 
VE Masaaki Kyoto Univ., Integrated Human Studies, Ass. Professor, 総合人間学部, 助教授 (80134443)

CoInvestigator(Kenkyūbuntansha) 
VSHIKI Shigehiro Kyoto Univ., Graduate School of Human and Environmental Studies Professor, 総合人間学部, 教授 (10093197)
日置 尋久 京都大学, 総合人間学部, 助手 (70293842)
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)
MORIMOTO Yoshinori Kyoto Univ., Integrated Human Studies, Professor, 総合人間学部, 教授 (30115646)

Project Fiscal Year 
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)

Keywords  homology 3sphere / Seifert manifolcl / cobordism / foliation / complex dynamical system / Ruelle operator / smoothing effect / hypoellipticity / ホモロジー3球面 / ザイフェルト多様体 / コボルディズム / 葉層構造 / 複素力学系 / Ruelle作用素 / 平滑化効果 / 準楕円性 / 4次元多様体 / SeibergWitten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 4manifolds, Ue showed the reciprocity for the values of W invariants of homology 3spheres. As its application, he showed that the W invariant of Seifert homology 3sphere coincides with its NeumannSiebenmann 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 1dimensional complex dynamical systems. He showed that dynamical zetafunctions 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
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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 microlocal 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
