2000 Fiscal Year Final Research Report Summary
A homology of orbifolds and related groups
| Project/Area Number |
11640071
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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 | Shizuoka University |
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Principal Investigator |
YOKOYAMA Misako Shizuoka University, Science, research assistant, 理学部, 助手 (80240224)
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| Co-Investigator(Kenkyū-buntansha) |
KUMURA Hironori Shizuoka University, Science, full-time lecturer, 理学部, 講師 (30283336)
OKUMURA Yoshihide Shizuoka University, Science, associated professor, 理学部, 助教授 (90214080)
IZAWA Tatsuo Shizuoka University, Science, associated professor, 理学部, 助教授 (20021941)
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| Project Period (FY) |
1999 – 2000
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| Keywords | orbifold / homology |
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| Research Abstract |
We define the PL-area of a 2-orbifold immersed in a 3-orbifold. We show that any two least area 2-orbifolds belonging to the class Ω do not intersect each other. The existence of the least area 2-orbifold is proved. And we obtain somes applications.
Waldhausen considered a certain class of 3-manifold called Haken manifolds, and classified it by their fundamental groups. Similary, Takeuchi classified a certain class of very good 3-orbifolds, and we classify much larger class of 3-orbifolds by their orbifold fundamental groups.
We introduce an orbifold composition and study their topology and the extensions and deformations of the maps between them. We obtain the theorems which yield the geometric realizations of amalgamated free products and HNN extensions of 3-orbifold fundamental groups. They are extensions of results of Feustel (1972,1973) and Feustel and Gregorac (1973).
We find spherical 2-orbifolds realizing the decomposition of the 3-orbifold fundamental groups, of which the amalgamated subgroups are isomorphic to the fundamental groups of orientable spherical 2-orbifolds. If one hypothesis fails, then there is a 3-orbifold which could not realize the given group decompositon. As an application we obatin a necessary and sufficient condition that unsplittable links embedded in S^3 are composite.
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