Solving the unknotting conjecture in dimension four and its development
Project/Area Number |
21540084
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Single-year Grants |
Section | 一般 |
Research Field |
Geometry
|
Research Institution | Hiroshima University |
Principal Investigator |
MATUMOTO Takao 広島大学, 大学院理学研究科, 名誉教授 (50025467)
|
Co-Investigator(Kenkyū-buntansha) |
KAMADA Seiichi 広島大学, 大学院理学研究科, 教授 (60254380)
|
Project Period (FY) |
2009 – 2012
|
Project Status |
Completed (Fiscal Year 2011)
|
Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
|
Keywords | 2次元結び目 / 2次元ブレイド / 4次元トポロジー / 数学史 / 2次元結び目 / 2次元ブレイド / チャート図の変形 / マルコフ型定理 / 4次元トポロジー / ケーリー図 / 和算と行列式 / 不変量 / 和算と行列式・ベルヌーイ数 / カスプ / 4次トポロジー |
Research Abstract |
The smooth unknotting conjecture in dimension four is reduced to the case which is connected by a one-parameter family with one intersection point to the unknot, by assuming our Markov type theorem. Moreover, since the reduced case can be studied by a kind of tree type Cayley diagram for the corresponding word problem, the conjecture is expected to be proved in a near future.
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Report
(4 results)
Research Products
(37 results)