Study in phantom of the quantum groups
Project/Area Number |
25610022
|
Research Category |
Grant-in-Aid for Challenging Exploratory Research
|
Allocation Type | Multi-year Fund |
Research Field |
Basic analysis
|
Research Institution | Waseda University |
Principal Investigator |
Murakami Jun 早稲田大学, 理工学術院, 教授 (90157751)
|
Project Period (FY) |
2013-04-01 – 2016-03-31
|
Project Status |
Completed (Fiscal Year 2015)
|
Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
|
Keywords | 量子群 / 結び目 / 低次元トポロジー / 体積予想 / 射影表現 / 結び目不変量 / 3次元多様体 / 表現論 / 結び目理論 / 量子展開環 / 双曲幾何学 |
Outline of Final Research Achievements |
Quantum groups whose quantum parameter q are roots of unity have projective representations which is not always semisimple. In this research, properties of such representations are studied, invariants of knots and 3-maniolfds related to such representations are constructed, and properties of such invariants are studied. Such invariant for knot is already constructed as the logarithmic invariant, and it is extended in this research to invariants of knots in 3-manifolds. The relation of logarithmic invariant and its generalization to the hyperbolic volume of the corresponding manifold is also given, which is a version of the volume conjecture of quantum invariants.
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Report
(4 results)
Research Products
(23 results)