2014 Fiscal Year Final Research Report
A study of the fiberedness and the genus using character varieties of knot groups
| Project/Area Number |
23540076
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Keio University (2012-2014)
Tokyo University of Agriculture and Technology (2011) |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2011-04-28 – 2015-03-31
|
| Keywords | 結び目群 / 指標代数多様体 / ねじれアレキサンダー不変量 |
|---|
| Outline of Final Research Achievements |
The purpose of this research was to construct a framework for detecting geometric properties of knots by some kind of finiteness using the character variety of the knot group and the twisted Alexander invariant. The results are as follows.
(1) We showed that the fiberedness and the genus of certain wide classes of knots (which include 2-bridge knots) are determined by information of the twisted Alexander invariant on a one dimensional irreducible component of the character variety.
(2) We gave an affirmative answer to a conjecture of Dunfield, Friedl and Jackson about the fiberedness and the genus of hyperbolic knots for an infinite family of 2-bridge knots.
|
| Free Research Field |
低次元トポロジー
|
