2004 Fiscal Year Final Research Report Summary
Classification of 3-manifolds by link correspondence and knot theory
| 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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| 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 |
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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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Research Products
(6 results)
