2016 Fiscal Year Final Research Report
The geometric structures of 3-manifolds and the asymptotic behavior of the Reidemeister torsion for linear representations
| Project/Area Number |
26800030
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Akita University |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Keywords | トポロジー / 三次元多様体 / ザイフェルト多様体 / ライデマイスタートーション / 基本群 / 線形表現 / 漸近挙動 / オービフォールド |
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| Outline of Final Research Achievements |
The geometric structures of 3-manifolds can be classified into the hyperbolic structures and the Seifert structures. This study has focused on 3-manifolds called Seifert manifolds, which admit Seifert structures, and determined the growth order of the asymptotic behavior of the higher-dimensional Reidemeister torsions and the limits of leading coefficients. Moreover the geometric meaning of the limit of leading coefficient was revealed. These results were derived from the explicit descriptions of the higher-dimensional Reidemeister torsions for Seifert manifolds.
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| Free Research Field |
幾何学
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