Calculations of twisted Novikov homology by using Heegaard splitting, and its applications
Project/Area Number |
21540071
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Single-year Grants |
Section | 一般 |
Research Field |
Geometry
|
Research Institution | Tokyo University of Agriculture and Technology |
Principal Investigator |
GODA Hiroshi 東京農工大学, 大学院・工学研究院, 教授 (60266913)
|
Project Period (FY) |
2009 – 2011
|
Project Status |
Completed (Fiscal Year 2011)
|
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)
|
Keywords | 微分トポロジ- / ノビコフホモロジー / ジョンソン準同型 / ヘガード分解 / ジョンソン-森田準同型 / 幾何学 / トポロジー / 結び目 / モース理論 |
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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Report
(4 results)
Research Products
(25 results)