On developments and applications of Heegaard theory
Project/Area Number |
21540082
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Single-year Grants |
Section | 一般 |
Research Field |
Geometry
|
Research Institution | Nara Women's University |
Principal Investigator |
|
Project Period (FY) |
2009 – 2012
|
Project Status |
Completed (Fiscal Year 2012)
|
Budget Amount *help |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
|
Keywords | 三次元多様体 / Heegaard 分解 / 距離 / ミウラ折り / Heegaard分解 / 相似構造 / Hempel distance / 安定写像 / graphic / 三次元双曲多様体 / 結び目 / 橋指数 / Heeaard分解 / Hemel distance |
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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Report
(5 results)
Research Products
(22 results)