2011 Fiscal Year Final Research Report
Calculations of twisted Novikov homology by using Heegaard splitting, and its applications
| Project/Area Number |
21540071
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Tokyo University of Agriculture and Technology |
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Principal Investigator |
GODA Hiroshi 東京農工大学, 大学院・工学研究院, 教授 (60266913)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 微分トポロジ- |
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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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