2012 Fiscal Year Final Research Report
On developments and applications of Heegaard theory
| Project/Area Number |
21540082
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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 | Nara Women's University |
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Principal Investigator |
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| Project Period (FY) |
2009 – 2012
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| Keywords | 三次元多様体 / Heegaard 分解 / 距離 / ミウラ折り |
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| Research Abstract |
In this research we first proved the following two results for Heegaard splitting of 3-manifold which is a generalization of 3-dimensional space: (1)Haken type theorem for essential laminations, and (2) existence of Heegaard splitting of distance n for each positive integer n. Then as an application of low dimensional topology, we gave: (3) a construction of generalized Miura map folding by using similarity structure on 2-dimensional torus.
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