Discrete quantization of low-dimensional geometry with quantum invariants
Project/Area Number |
25287014
|
Research Category |
Grant-in-Aid for Scientific Research (B)
|
Allocation Type | Partial Multi-year Fund |
Section | 一般 |
Research Field |
Geometry
|
Research Institution | Waseda University |
Principal Investigator |
Murakami Jun 早稲田大学, 理工学術院, 教授 (90157751)
|
Co-Investigator(Kenkyū-buntansha) |
水澤 篤彦 早稲田大学, 理工学術院, 助教 (50707726)
|
Project Period (FY) |
2013-04-01 – 2017-03-31
|
Project Status |
Completed (Fiscal Year 2016)
|
Budget Amount *help |
¥8,320,000 (Direct Cost: ¥6,400,000、Indirect Cost: ¥1,920,000)
Fiscal Year 2016: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2015: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2014: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2013: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
|
Keywords | 低次元トポロジー / 量子不変量 / 双曲幾何学 / 3次元多様体 / 結び目 / 体積予想 / 量子群 / 射影表現 / 結び目不変量 / 結び目理論 / 双曲幾何 / 量子展開環 / 表現論 |
Outline of Final Research Achievements |
The aim of this research is to construct discretized quantum geometry for 2 and 3 dimensional case. To do this, various quantum invariants and their relations are studied. For example, we study the colored Jones invariant, the colored Alexander invariant, the Hennings invariant and the logarithmic invariant. Quantum invariants for knotted graphs and its relation to the geometric structure is also studied. Especially, we get the relation between quantum invariants and hyperbolic volume determined by the geometric structure for various quantum invariants.
|
Report
(5 results)
Research Products
(42 results)