2011 Fiscal Year Final Research Report
Studies on partial orders on sets of 3-manifolds defined by epimorphisms between fundamental groups.
| Project/Area Number |
21540100
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Soka University |
|---|
Principal Investigator |
|
|---|
| Co-Investigator(Renkei-kenkyūsha) |
MORIFUJI Takayuki 慶應義塾大学, 経済学部, 教授 (90334466)
SUZUKI Masaaki 秋田大学, 教育文化学部, 准教授 (70431616)
|
|---|
| Project Period (FY) |
2009 – 2011
|
| Keywords | 3次元多様体 / 結び目 / 基本群 |
|---|
| Research Abstract |
For the set of prime knots with up to 11-crossings, we determined the partial order relation defined by using meridian preserving epimorphisms between knots groups. We also proved that for any given 2-bridge knot there exists a Montesinos knot with an epimorphims which is induced by a degree zero map. Further we found pairs of a 3-bridge hyperbolic Montsinos knot and a 2-bridge hyperbolic knot which is not induced from a nonzero degree map. For any knot, there exists a infinitely many prime numbers such that there exists a non abelian representation on its knot group in 2-dimensional special linear group over a finite prime field with such a characteristic.
|
