| 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)
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| 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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