Study of positive knots via contact structures
| Project/Area Number |
16H07230
|
|---|
| Research Category |
Grant-in-Aid for Research Activity Start-up
|
| Allocation Type | Single-year Grants |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Tokyo University of Science |
|---|
Principal Investigator |
Tagami Keiji 東京理科大学, 理工学部数学科, 助教 (60778174)
|
|---|
| Project Period (FY) |
2016-08-26 – 2018-03-31
|
| Project Status |
Completed (Fiscal Year 2017)
|
| Budget Amount *help |
¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
|
|---|
| Keywords | 結び目 / 正結び目 / 接触構造 / ラグランジアン充填 / 正絡み目 / サーストン・ベネカン数 |
|---|
| Outline of Final Research Achievements |
A knot is a smooth embedding of a circle into the 3-dimensional Euclidean space. A knot is Lagrangian fillable if it bounds an oriented Lagrangian surface from below in the symplectisation of the standard contact structure of the 3-dimensional Euclidean space.
Hayden and Sabloff proved that any positive knot is Lagrangian fillable. Inspired by their work, in this study, I investigated relations between the Lagrangian fillability and the positivity of knots. As a result, I proved that (1) any almost positive knot with a certain condition on its Seifert graph is Lagrangian fillable, (2) any alternating and Lagrangian fillable knot is positive.
|
Report
(3 results)
Research Products
(2 results)
