Singularity theory of mappings from the viewpoint of low-dimensional topology
Project/Area Number |
22540074
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Single-year Grants |
Section | 一般 |
Research Field |
Geometry
|
Research Institution | Seikei University (2011-2014) Shinshu University (2010) |
Principal Investigator |
|
Project Period (FY) |
2010-04-01 – 2015-03-31
|
Project Status |
Completed (Fiscal Year 2014)
|
Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
|
Keywords | 多様体 / 微分位相幾何学 / 微分可能写像 / 特異点 / はめ込み / Thom多項式 / 結び目 / 戸田括弧積 / 折り目写像 / ボルディズム / コボルディズム / 戸田ブラケット |
Outline of Final Research Achievements |
I studied various topics related to singularities of differentiable mappings in order to have new knowledge on differential topology. First, I studied immersions (ie maps with no singularities) between smooth manifolds, using (mainly global aspects of) singularity theory, and published two journal articles. Next, I studied fold maps (smooth maps with only "the mildest" singularities called fold singularities), and published two journal articles. Moreover, I published another journal article on a certain transformation of diagrams of classical knots. I also began to study surface-knots in the last year of the program.
|
Report
(6 results)
Research Products
(11 results)