2009 Fiscal Year Final Research Report
Applications of centers of mass configuration spaces to homotopy theory
| Project/Area Number |
18540092
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | University of the Ryukyus |
|---|
Principal Investigator |
KAMIYAMA Yasuhiko University of the Ryukyus, 理学部, 教授 (10244287)
|
|---|
| Project Period (FY) |
2006 – 2009
|
| Keywords | 重心配置空間 / クモの巣装置 / モーメント角複体 |
|---|
| Research Abstract |
Homotopy theory is a topology which studies continuous maps between two spaces. Traditionally, problems in homotopy theory have been solved by ad hoc methods. In the present research, I defined the "centers of mass" configuration spaces and posed a conjecture about its property. I elucidated that if our conjecture was proved, then not only many known results are reproved in an integral way, but also we can prove unsolved problems.
The merit of our research is as follows. The complement of hyperplanes in the Euclidean space is a computable object. Since our configuration space is a kind of such a complement, our conjecture is far more accessible than the traditional way to construct continuous maps.
|
Research Products
(17 results)
