2017 Fiscal Year Final Research Report
Representation theoretical analysis of the knot contact homology
Project/Area Number |
26800046
|
Research Category |
Grant-in-Aid for Young Scientists (B)
|
Allocation Type | Multi-year Fund |
Research Field |
Geometry
|
Research Institution | Meijo University |
Principal Investigator |
|
Project Period (FY) |
2014-04-01 – 2018-03-31
|
Keywords | 結び目 / 基本群 / トレースフリー表現 / 指標多様体 / コンタクトホモロジー / 2重分岐被覆 / 幽霊指標 |
Outline of Final Research Achievements |
This project focuses on a representation theoretical mechanism relating the abelian knot contact homology and the character ring of the 2-fold branched cover of a 3-sphere branched along a knot. This relationship was conjectured by L. Ng, and it has been established by him for 2-bridge knots. In this project, we first introduced a new notion called a ghost character of a knot, which gives an obstruction for the conjecture to be true. Using it, in a joint work with Shinnosuke Suzuki, who was a graduate student at Meijo University, we found a counterexample of the conjecture for some torus knots. We are still researching this relationship to reveal the representation theoretical mechanism of the knot contact homology completely.
|
Free Research Field |
低次元位相幾何学
|