| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2011: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Research Abstract |
We focus on homologically fibered knots, and we calculate some invariants for them concretely. We proved that the abelian quotients of monoids of homology cylinders are not finitely generated by using the sutured Floer homology. It turned out that a half-transversal flow needed to satisfy a condition when we calculated the twisted Novikov homology by using a Heegaard splitting associated with the flow. We define the notion J(K) for a knot K using the Johnson homomorphisms. If a knot K is fibered, J(K)=∞. We show that there are infinitely many non-fibered homologically fibered knots with J(K)=∞.
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