2011 Fiscal Year Final Research Report
Homotopy theory on singularities of differentiable maps and K-invariant spaces of the jet spaces
| Project/Area Number |
21540085
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Yamaguchi University |
|---|
Principal Investigator |
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
KOMIYA Katuhiro 山口大学, 名誉教授 (00034744)
MIYAZAWA Yasuyuki 山口大学, 大学院・理工学研究科, 教授 (60263761)
NAITOH Hiroo 山口大学, 大学院・理工学研究科, 教授 (10127772)
KIUCHI Isao 山口大学, 大学院・理工学研究科, 教授 (30271076)
KAJI Shizuo 山口大学, 大学院・理工学研究科, 講師 (00509656)
IIYORI Nobuyasu 山口大学, 教育学部, 教授 (00241779)
SATO Yoshihisa 九州工業大学, 情報工学部, 教授 (90231349)
|
|---|
| Project Period (FY) |
2009 – 2011
|
| Keywords | 特異点 / 可微分写像 / ホモトピー / 折り目 / コボルディズム. |
|---|
| Research Abstract |
We first proved that there exists an isomorphism of the group of oriented cobordism classes of fold maps of closed oriented n-manifolds to the given oriented closed manifold P of degree$ 0$ to the homotopy group of P to the well-known space F. An element of the n-th stable homotopy group of spheres can be possibly detected by singularities of some extension of a corresponding fold map. We tried to solve this problem in the higher dimensions. Two types of singularities of maps between 4q-manifolds whose Thom polynomials with integer coefficients have nonvanishing coefficients of the leading Pontrjagin class P_{ q} can detect elements of J-images.
|
