A study on homotopy sets and families of homotopy invariant subsets
| Project/Area Number |
15K04884
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Fukuoka University |
|---|
Principal Investigator |
ODA Nobuyuki 福岡大学, 理学部, 教授 (80112283)
|
|---|
| Project Period (FY) |
2015-10-21 – 2019-03-31
|
| Project Status |
Completed (Fiscal Year 2018)
|
| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
|
|---|
| Keywords | 幾何学 / トポロジー / 自己ホモトピー同値写像 / 自己親密数 / K群 / ファイブレイション / コファイブレイション / コゴットリーブ集合 / コゴトリーブ集合 / コファイブレーション / コゴットリーブ群 / ホモトピー同値 |
|---|
| Outline of Final Research Achievements |
A theorem is proved on the relation between cofibrations and the self-closeness numbers, and its dual, that is, a theorem on the relation between fibrations and the self-closeness numbers. The K group of the ring of continuous functions for spaces with special conditions is presented by cohomology groups. A result is proved on the homotopy set of maps which preserve cyclic elements and its dual. A theorem is proved about the groups of the self homotopy equivalences of smash products of a space and the semi-direct products of the direct product of the groups of the self homotopy equivalences of the space and the symmetric groups, and moreover, some general results are proved making use of cohomology groups.
|
| Academic Significance and Societal Importance of the Research Achievements |
自己親密数に関する結果は新しい結果であり，特に，コファイブレイションおよびファイブレイションと自己親密数に関する定理は今後の研究に有用である．連続関数環のK群に関する結果，サイクリック元を保存する写像のホモトピー集合とその双対の結果，コゴトリーブ集合について特別な場合に短完全列が存在すること，空間の約積の自己ホモトピー同値写像類の群と空間の自己ホモトピー同値写像類の群と対称群の半直積との関係を与える定理は新しい研究の基礎となる結果であり，これらの分野の今後の研究に役立つ．
|
Report
(5 results)
Research Products
(10 results)
