多様体のホモトピー論的研究
著者 石本 浩康
著者別表示 Ishimoto Hiroyasu
雑誌名 平成13(2001)年度 科学研究費補助金 基盤研究(C) 研究概要
巻 1999 2001
ページ 2p.
発行年 2003‑09‑16
URL http://doi.org/10.24517/00063869
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2001 Fiscal Year Final Research Report Summary
Homotopy theoretical research of manifolds
Research Project
Project/Area Number
11640069
Research Category
Grant-in-Aid for Scientific Research (C)
Allocation Type
Single-year Grants
Section
⼀般
Research Field
Geometry
Research Institution
Kanazawa University
Principal Investigator
ISHIMOTO Hiroyasu Kanazawa Univ., Fac. Science, Prof., 理学部, 教授 (90019472)
Co-Investigator(Kenkyū-buntansha)
TOMARI Masataka Kanazawa Univ., Fac. Science, Assoc. Prof., 理学部, 助教授 (60183878) MORISHITA Masanori Kanazawa Univ., Fac. Science, Assoc. Prof., 理学部, 助教授 (40242515) SUGANO Takashi Kanazawa Univ., Fac. Science, Prof., 理学部, 教授 (30183841)
IWASE Zunici Kanazawa Univ., Fac. Science, Research Assoc., 理学部, 助⼿ (70183746) FUJIOKA Atsushi Kanazawa Univ., Fac. Science, Assoc. Prof., 理学部, 講師 (30293335)
Project Period (FY)
1999 – 2001
Keywords
primary manifolds / homotopy equivalent manifolds / constant mean curvature surfaces / harmonic inverse mean curvature surfaces / hypersurface isolated singularities / Milnor number / Pn'mes and Knots / automorphic forms
Research Abstract
(1) Ishimoto studied the problem whether the matter corresponding to the Poincare conjecture holds or not for primary manifolds which are m-spheres with attached q- handles in the metastable range. For that purpose, he intended to extend the James-Whitehead theorem to the one for primary manifolds and succeeded in such case that the quadratic forms which distinguish primary manifolds take values in a cyclic group. Using the result, he proved in almost all cases that the matter in question also valid
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Published: 2003-09-16
Research Products
(12 results)All Other All Publications
URL: https://kaken.nii.ac.jp/report/KAKENHI-PROJECT-11640069/116400692001kenkyu_seika_hokoku_
when the cyclic group is Z_<24>, adding to the results already obtained.
(2) Fujioka studied the fundamental properties of harmonic inverse mean curvature surfaces which are natural generalization of constant mean curvature surfaces. In particular, he characterized such a surface as the one which admits a transformation preserving a certain quantity represented with curvature. He studied also the Bonnet surfaces.
(3) Tomari studied the theory of multiplicity of filtered rings, and as an application, he constructed a criterion formula for the Milnor number of f which gives the definition of hyper surface isolated singularities, using the weight of coordinates and the Taylor expansion.
(4) Morishita studied analogies between knots and primes, 3-manifolds and number fields, basing on the analogy between link groups and Galois groups, and tried to bridge between the algebraic number theory and the 3-dimensional topology. He also studied with K, Murasugi in Toronto.
(5) Sugano studied the automorphic forms on unitary groups of degree 3 in number theory. He gave the explicit expansion for Eisenstein series and Kudla lift images using primitive theta functions, and gave the non-vanishing condition for the Kudla lift in terms of the periods.
[Publications] A.Fujioka: "Timelike Bonnet Surfaces in Lorentzian Space Forms"Differential Geometry and its Applications. (to apper). [Publications] A.Fujioka: "Timelike surfaces with harmonic inverse mean curvature"Advanced Studies in Pure Mathematics. (to apper).
[Publications] M.Tomari: "Cyclic covers of normal graded rings"Kodai Math. J.. 24. 436-457 (2001)
[Publications] M.Tomari: "Multiplicity of filtered rings and simple K3 singularities of multiplicity two"Publ. RIMS Kyoto Univ. (to apper). [Publications] M.Morishita: "A theory of genera for cyclic coverings of links"Proc. Japan Academy. 77. 115-118 (2001)
[Publications] S.Kato: "Whittaker-Shintani functions of orthogonal groups"Tohoku Math. J.. (to apper).
[Publications] A. Fujioka: "Timelike Bonnet Surfaces in Lorentzian Space Forms"Differential Geometry and its Applications. (to appear). [Publications] A. Fujioka: "Timelike surfaces with harmonic inverse mean curvature"Advanced Studeis in Pure Mathematics. (to appear).
[Publications] M. Tomari: "Cyclic covers of normal graded rings"Kodai Math. J.. 24. 436-457 (2001)
[Publications] M. Tomari: "Multiplicity of filtered rings and simple K3 singularities of multiplicity two"Publ. RIMS Kyoto Univ.. (to appear). [Publications] M. Morishita: "A theory of genera for cyclic coverings of links"Proc. Japan Acad.. 77. 115-118 (2001) [Publications] S. Kato: "Whittaker-Shintani functions for orthogonal groups"Tohoku Math. J.. (to appear).
