2011 Fiscal Year Final Research Report
A research of open book decomposition of 3-manifolds
| Project/Area Number |
22740049
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Gunma University (2011)
Ritsumeikan University (2010) |
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Principal Investigator |
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| Project Period (FY) |
2010 – 2011
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| Keywords | 3次元多様体 / オープンブック分解 / Alexander多項式 |
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| Research Abstract |
It has become clear that the Alexander polynomial (equivalently the Conway polynomial) of open book decompositions plays an effective role for an estimation of the complexity of open book decompositions, which we defined in our previous research. From this observation, we have obtained a prediction that the Johnson-Morita representation of the mapping class group of the fiber surface of an open book decomposition will be useful to constract a new invariant of open book decomposition which gives us stricter estimation of the complexity than the Alexander polynomial.
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