| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Research Abstract |
We did research rerated to the ‘Volume Conjecture’ which gives a relation between the quantum invariant related to the quantum group Uq(sl2), and, by noticing the non-semisimple representation of it, such representations and the related knot invariants were studied. By applying the volume conjecture, the geometric structure of a knot complement and the volumes of polyhedrons in a three space with a constant curvature were studied. Moreover, new invariants of knots in a three manifolds were constructed from the non-semisimple representations.
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