1999 Fiscal Year Final Research Report Summary
Research for low-dimensional manifdds with various geometric structures
| Project/Area Number |
10640074
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Kyoto University |
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Principal Investigator |
VE Masaaki Kyoto Univ., Integrated Human Studies, Ass. Professor, 総合人間学部, 助教授 (80134443)
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| 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)
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| Project Period (FY) |
1998 – 1999
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| Keywords | homology 3-sphere / Seifert manifolcl / cobordism / foliation / complex dynamical system / Ruelle operator / smoothing effect / hypoellipticity |
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| 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
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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 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
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