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 |
Research Field |
Geometry
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Research Institution | Akita University |
Principal Investigator |
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Project Period (FY) |
2014-04-01 – 2017-03-31
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Project Status |
Completed (Fiscal Year 2016)
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Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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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 / 幾何構造 / オイラー標数 / ザイフェルト構造 / 双曲構造 / 位相不変量 / 増大度 |
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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Report
(4 results)
Research Products
(11 results)