1999 Fiscal Year Final Research Report Summary
Studies on Combinatorial Structures of 3-Manifolds
| Project/Area Number |
10640089
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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 | Keio University |
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Principal Investigator |
ISHII Ippei Keio Univ., Dept.of Math., Associate Prof., 理工学部, 助教授 (90051929)
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| Co-Investigator(Kenkyū-buntansha) |
OHTA Katsuhiro Keio Univ., Dept.of Math., Associate Prof., 理工学部, 助教授 (40213722)
ENOMOTO Hikoe Keio Univ., Dept.of Math., Prof., 理工学部, 教授 (00011669)
MAEDA Yoshiaki Keio Univ., Dept.of Math., Prof., 理工学部, 教授 (40101076)
KOUNO Masaharu Kitami Inst.of Tech., Dept.of Information, Prof., 教授 (40170203)
IKEDA Hiroshi Keio Univ., Dept.of Math., Prof., 理学部, 教授 (10031353)
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| Project Period (FY) |
1998 – 1999
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| Keywords | 3-manifold / spine / Heegaard splitting / Dehn surgery / Poincare conjecture |
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| Research Abstract |
(1) On Ds-diagrams
It was shown that two Ds-diagrams representing the same closed 3-manifold can be transformed to each other by a sequence of "elementary deformations".
(2) On Heegaard splittings
A new condition for a Heegaard splitting to be reducible has been found. This condition is described by the notion of a "d-pseudo core".
(3) On framed links in a homotopy 3-sphere
It was shown that any homotopy 3-sphere admits a "very special framed link" , which enjoys a good property and closely related to a Heegaard splitting.
(4) On the Poincare conjecture
Using the above two results (2) and (3), we have proposed a new method for attacking the famous "Poincare conjecture".
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