| Project/Area Number |
14540088
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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 | Osaka City University |
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Principal Investigator |
KAWAUCHI Akio Osaka City Univ., Science, Professor, 大学院・理学研究科, 教授 (00112524)
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| Co-Investigator(Kenkyū-buntansha) |
KANENOBU Taizo Osaka City Univ., Science, Assoc. Professor, 大学院・理学研究科, 助教授 (00152819)
KAMADA Seiichi Hiroshima Univ., Science, Professor, 大学院・理学研究科, 教授 (60254380)
IMAYOSHI Yoichi Osaka City Univ., Science, Professor, 大学院・理学研究科, 教授 (30091656)
HASHIMOTO Yoshitake Osaka City Univ., Science, Assoc. Professor, 大学院・理学研究科, 助教授 (20271182)
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| Project Period (FY) |
2002 – 2004
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| Project Status |
Completed (Fiscal Year 2004)
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| Budget Amount *help |
¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 2004: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2003: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2002: ¥1,300,000 (Direct Cost: ¥1,300,000)
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| Keywords | Integral lattice / Prime link table / 3-manifold table / Reni-Mecchia-Zimmermann's conjecture / double branched covering / hyperbolic manifold / surface-knot / triple point canceling number / Conwayの絡み目表 / 3次元多様体 / 絡み目 / 格子点 / イミテーション理論 / 結び目 / アーフ不変量 / 曲面絡み目 / linking不変量 / デーン手術 / Gordon-Luecke定理 / 3次元多様体の分類 |
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| Research Abstract |
For our establishing canonical correspondences from the set of closed connected oriented 3-manifolds to the set of prime links and from the set of prime links to the delta set of integral lattice points, we completed the correspondence classifications for the integral lattice points of lengths up to 7. By joint works with Dr.I.Tayama, we completed the correspondence classification from the set of the prime links of lengths 8,9,10 to the delta set of integral lattice points. On Reni-Mecchia-Zimmermann's conjecture, the head investigator solved this conjecture affirmatively. Also, the head investigator estimated the triple point canceling number of a surface-knot and constructed an example of surface-knots with a sufficiently large difference between the triple point canceling number and the triple point number.
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