2018 Fiscal Year Final Research Report
Research on Hempel distances of 3-manifolds by using the detailed properties of the curve complex
| Project/Area Number |
15H06284
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Aichi University of Education |
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Principal Investigator |
Ido Ayako 愛知教育大学, 教育学部, 助教 (00759532)
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| Research Collaborator |
KOBAYASHI Tsuyoshi
JANG Yeonhee
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| Project Period (FY) |
2015-08-28 – 2019-03-31
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| Keywords | ３次元多様体 / Heegaard分解 / ヘンペル距離 / 曲線複体 |
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| Outline of Final Research Achievements |
In this research, we improved the techniques to construct geodesics in the curve complex. In the process, we introduced a new concept on Heegaard splitting, called "keen", and showed that there exists a keen Heegaard splitting with Hempel distance n for any integer n>1. Moreover, we expanded this concept to bridge splittings.
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| Free Research Field |
位相幾何学
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| Academic Significance and Societal Importance of the Research Achievements |
曲線複体は３次元多様体，クライン群, 写像類群，タイヒミュラー空間の研究などに幅広く活用されている．特に最近はHeegaard分解に限らず，多くの分野の懸案が曲線複体の概念を用いた手法を利用することにより解決されている．従来とは異なる，細密な幾何学の観点から曲線複体を研究することで得られた本研究の成果は，ヒーガード分解に限らず，関連する他の分野にも新たな展開をもたらすことが期待される．
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