Characteristic classes of quandles, and its applications to low dimensional topology
Project/Area Number |
25800049
|
Research Category |
Grant-in-Aid for Young Scientists (B)
|
Allocation Type | Multi-year Fund |
Research Field |
Geometry
|
Research Institution | Kyushu University |
Principal Investigator |
|
Project Period (FY) |
2013-04-01 – 2017-03-31
|
Project Status |
Completed (Fiscal Year 2016)
|
Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
|
Keywords | 幾何学 / トポロジー / カンドル / 結び目 / コホモロジー / 数学 / べき零群 / 結ぶ目 |
Outline of Final Research Achievements |
The subject of this research is "a quandle", which is an algebraic system. The purpose is to explore quandle theory from broad viewpoints and by many means. I gave some applications to low dimensional topology, including 3-manifold, (surface) knots, branched covering space, Lefschetz fibrations, and surface braids. The study of quandle contains many mysterious areas; however, I showed that homotopy theory, group cohomology, bordism groups, invariant theory, algebraic K-theory are useful to quandle theory. Furthermore, as an unexpected development, I also pointed out that quandle theory is compatible with secondary characteristics, bilinear forms, and cup products.
|
Report
(5 results)
Research Products
(10 results)