| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
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| 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.
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